## Indifference Curve Questions and Answers

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Consumers buy both alcoholic and nonalcoholic beverages. If the government tries to discourage people from drinking alcoholic beverages by imposing an excise tax on them but gives consumers an inco...

An indifference curve is: a) a collection of market baskets that are equally desirable to the consumer b) a collection of market baskets that the consumer can buy c) a curve whose elasticity is con...

Indifference curves that intersect would be illogical constructs because: a) more is better than less b) of diminishing marginal utility c) of the transitivity property of indifference theory d) of...

Consider the following utility function: U(X, \: Y) = 5X + 2Y. Derive the equation for the indifference curve where utility is equal to a value of 100.

Consider the following utility function: U(X, \: Y) = X^{0.33}Y^{0.67}. Derive the equation for the indifference curve, where utility is equal to a value of 100.

Consider the following utility function: U(X, \: Y) = 10X^{0.5} + 5Y. Derive the equation for the indifference curve, where utility is equal to a value of 100.

Which of the following statements about indifference curves is not true? a. Every indifference curve intersects the consumer's budget line at least once. b. Indifference curves slope downward. c....

Consider the function f(x) = 4x + 1 + 20/x. Find f'(x) and draw its sign diagram.

The government rations the amount of gasoline that consumers can purchase. A consumer who would have purchased more than the rationed amount of gasoline will instead, ______. A. purchase more gasol...

What are the different uses of Indifference Curve Analysis?

State all the properties of an indifference curve.

What is the difference between an indifference curve and an indifference map?

True or False: The marginal rate of technical substitution tells the rate at which the firm is able to exchange inputs at the prevailing input price ratio keeping output fixed.

In economics, what is an "indifference curve"?

A sequence {a_n} is called monotonic, if it is either increasing or decreasing. (a) True (b) False

Let y=5-x^4. Determine the interval where the function is decreasing.

Define the term "indifference curve" in economics.

Why does total utility increase as the consumer moves to indifference curves further from the origin?

What are the differences between an indifference curve and an isoquant? What specifically are the slopes of each?

Is it possible for indifference curves to intersect? Explain.

The Hicks version of substitution effect of a price change measures the change in a consumer's demand if the consumer's income were changed just enough so the consumer would remain on the same indi...

Discuss the characteristics of indifference curves.

Suppose you have a two-good world, good X and good Y, and a utility function U=xy. On a graph, draw the indifference curve for total utility equal to 100.

What is your understanding of an indifference curve?

What are the major assumptions of an indifference curve?

The indifference curve is used theoretically to demonstrate consumers' level of satisfaction at varied units of consumption. Discuss the key assumptions behind the use of indifference curves.

Use the provided graph and determine the interval where the function is decreasing.

Let f(x) = (x - 1)(x+2)x6. Find the interval of decreasing function.

Sammy Sleaze has decided to illegally copy CDs to sell in his CD store. There are several possible CD copiers that sales reps have shown him. Machine A has a fixed cost of $900 with a variable cost...

True or False: Even holding risk/liquidity/taxes constant, bonds of different maturities are not perfect substitutes for one another.

Along the indifference curve, _____. a. marginal utility falls b. total utility is constant c. total utility decreases at a decreasing rate d. marginal utility is constant

Sketch the curve y = x^4 - 8 x.

How does a higher indifference curve represent higher levels of satisfaction?

What are the characteristics of an indifference curve?

An indifference curve illustrates: a. a firm's profits. b. a consumer's budget. c. a consumer's preferences. d. the prices of two goods.

Let f(x) = 3 + 6x - x3. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). Determine the interval where f is increasing.

What are the assumptions of an indifference curve?

Perform a first derivative test on the function f x = 4x^5 - 25x^4 + 40x^3 + 5 -1, 4. a. Locate the critical points of the given function. b. Use the First Derivative Test to locate the local max...

Find the interval s where the function is increasing and the interval s where it is decreasing. g x = 2x - x^3

Consider the function f(x) = 12x^{2/3}. (a) Give the intervals of increase and decrease of f(x). (b) Give the maximum and minimum values of f(x).

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A set of indifference curves with each successive curve lying outside the previous one in a North East direction is called?

Let f(x)=10x^3/x^2-1, and find the intervals where f is increasing or decreasing.

(a) Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant, and (b) make a table of values to verify whethe...

If Qs = -20 + 10p, and Qd = 400 - 20p, what is the equilibrium price? A. 38 B. 12.67 C. 14 D. 42

An indifference curve represents bundles of goods that a consumer: A. ranks from most preferred to least preferred. B. views as equally desirable. C. refers to any other bundle of goods. D. All of...

Bezier curves are used in computer-aided design and are named after the French mathematician Pierre Bézier (1910-1999), who worked in the automotive industry. A cubic Bézier curve is...

What information is contained in an indifference curve? Why are such curves (a) downsloping (b) convex to the origin?

Consider two bundles of coffee and chocolate and how Ted feels about them. The first bundle consists of two cups of coffee and two chocolate bars. The second bundle consists of one cup of coffee an...

Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then find the open intervals analytically. \ y = \dfrac{x^2}{2x-1}

Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then find the open intervals analytically. \ f(x) = \dfrac{x^3}{4} - 3x

Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then find the open intervals analytically. \ f(x) = x^4-2x^2

Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then find the open intervals analytically. \ f(x) = \dfrac{1}{(x+1)^2}

An indifference curve identifies the: a. utility maximizing bundle of goods that the consumer will purchase. b. bundles of goods that can be purchased with a given amount of income. c. bundle of go...

State the Increasing/Decreasing Test.

Find the acute angles between the curves at their points of intersection. y = sin x, y = cos x, 0 less than equal to x less than equal to pi/2. (The angle between two curves is the angle between th...

Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) less than 0 and f''(x) less than 0 for all x. (b) f'(x) greater than 0 and f''(x) greater than 0 for all x.

Find the area of the region that lies inside both curves. r = a*sin theta, r = b*cos theta, a greater than 0, b greater than 0.

Find {dy} / {dx} and {d^2y} / {dx^2}. For which values of t is the curve concave upward? x = t^2 + 1, y = t^2 + t

If S and F are perfect complements you must be indifferent between these two bundles: One unit of S and one unit of F & Two units of S and one unit of F. True False

What do we call the magnitude of the slope of an indifference curve?

What assumptions are necessary to prevent indifference curves from crossing? A. Transitivity. B. Completeness. C. More is better. D. Transitivity and more is better.

Marie has a weekly budget of $24, which she likes to spend on magazines and pies. 1) If the price of a magazine is $4 each, what is the maximum number of magazines she could buy in a week? 2) If th...

Refer to the table of three market baskets above. Which of the following is false? A. consumer could be indifferent between A and B. B. A and C could be on the same indifference curve. C. The consu...

Which of the following is true about the indifference curve where one commodity (such as pollution) is bad? A. It has a negative slope. B. It has a positive slope. C. It is horizontal. D. It is ver...

True or false? If the price the U.S. Postal Service charges to deliver Express Mail rises, the demand facing Federal Express will fall because their respective services are complementary.

Saccharin and aspartame are both low-calorie substitutes for sugar. If saccharin is found to cause cancer: a. the price of aspartame will increase. b. the price of sugar will decrease. c. the price...

True or false? As more close substitutes become available, demand tends to be more price elastic.

If indifference curves are concave to the origin, which assumption of preferences is violated?

The point (2, -4) is an extreme value of the function f (x) = a /pi sin(pi x) - bx. Then - 4a + 3b = a. -14. b. 2. c. 14. d. -2.

An increase in the price of iPhones causes the demand for Samsung Galaxys to increase because these two goods are: a. complementary b. coexistent c. substitutes d. interchangeable

When the price of hot dogs decreases, what happens in the market for the complementary good of hot dog buns? a. demand decreases, decreasing price and quantity b. supply decreases, decreasing price...

Based on the following table of yearly revenues, do you think the two teams are complements or substitutes? Why? Year Manatees Gemini 2005 $10 $10 2006 $5 $15 2006 $15 $20 2008 $25 $35 2009 $12 $12...

Susan Meyer, the owner/manager of Meyer's Motor Court in Key West, Susan Meyer is considering outsourcing the daily room cleanup for her motel to Duffy's Maid Service. Susan rents an average of 50...

Which of the following statements concerning indifference curves is true? a. An indifference curve is the locus of points describing proportional price levels of the two goods. b. Indifference curv...

If a consumer does not have convex preferences, then a point of tangency between her indifference curve and her budget line must be an optimal bundle. A) True B) False

Kimberly Clark in Neenah, WI manufactures paper towels and sells them for $1.00 per roll. The company's variable cost is $0.20 per roll. The Neenahlocation has a fixed cost of $25,000 (rent, utilit...

Suppose you allocate all your wealth to "housing" and "savings". Housing costs $40 per square foot. You have $100,000 in wealth and have elected to build a 1000 square foot house. Draw your budget...

The William Company manufactures personal-sized drip coffee makers. The coffee makers sell for $25. At present, the coffee makers are manufactured in a small plant that relies on direct labor worke...

True or False: \\ Perfect substitutes always have exactly one bundle which is optimal.

True or false? Perfect substitutes are associated with linear isoquants.

An indifference curve is a line that shows combinations of among which a is indifferent. a. prices; producer b. goods; consumer c. prices; consumer d. goods; producer

Which of the following is NOT a property of isoquants? A. They have a downward slope. B. They do not cross. C. They are "thin." D. The closer they are to the origin, the higher the level of output.

Latanya likes to talk on the telephone. We can represent her preferences with the utility function U(B, J) = 18B + 20J, where ''B'' and ''J'' are minutes of conversation per month with Bill and Jac...

Suppose there are two types of food, meat and bread. Draw the indifference curve for the following consumer: Taxa, a sumo wrestler, cares only about the number of calories he consumes; he wants to...

Suppose there are two types of food, meat and bread. Draw the indifference curve for the following consumer: Mia is a vegetarian who doesn't care (one way or the other) about meat.

John's MRS for reading books with watching movies is three movie per book, regardless of the amounts consumed. What is the formula for his family of indifference curves? What do these curves look l...

Suppose bundled A and B lie on the same indifference curve. Bundle C lies between bundles A and B, on a straight line that connects them. The consumer's preferences satisfy the Declining MRS Princi...

True, false, or uncertain. Explain. \\ All else equal, a person with steep indifference curves is less likely to participate in the labor market than a person with a flatter indifference curve.

What is the difference in shape between conventional (concave) indifference curves, indifference curves associated with perfect substitution, indifference curves associated with perfect complements...

The town of Greenville has three families, each with one child, and each of which earns $20,000 per year (pre-tax). Each family is taxed $4,000 per year to finance the public school system in the t...

Using diagrams and appropriate assumptions, explain why two indifference curves cannot intersect.

Consider a consumer with a utility function over two goods, x and y, given by U(x, y) = 9x^(1/3) y^(2/3). Suppose our consumer has an income of $60, the price of good x is $4 and the price of good...

Initially, the consumer's income is M = $500, the price of food is $10/unit, and the price of all other goods is $1/unit. Compare two alternative government programs, program (A): The consumer rece...

Wendy has $70.00 a month to spend on the soap and coffee she needs to function properly. Draw Wendy's budget constraint, assuming the soap costs $3.50, and the coffee costs $14.00 a pound.

Use indifference curve analysis to show how the Social Security pension system can reduce annual consumption for some workers who have strong preference for current versus future consumption. What...

If two goods are perfect complements, then: a. the marginal rate of substitution is constant. b. the indifference curves are straight lines. c. the indifference curves are L-shaped. d. Both (a) an...

A college student has two options for meals: eating at the dining hall for $6 per meal or eating a Cup O'soup for $1.50 per meal. His weekly food budget is $60. Draw the budget constraint showing...

Community indifference curves are _____ sloped and _____ to the origin. A) positively, concave B) negatively, convex C) positively, convex D) negatively, concave

The curve which shows the possible combination of two commodities, each yielding the same satisfaction or utility to the consumer is known as A. Demand curve B. Difference curve C. Indifference cur...

Indifference curves usually slope downward (from left to right) because: a. the marginal utility of consumption is usually positive. b. the marginal utility of consumption is always positive. c....

Homer, a very special fellow, has very special preferences. He normally likes to consume beer and donuts. However, if he consumes more than 12 bottles of beer, he enters a state of stupor and does...

Phillip's utility function is given by U(x,y)=min{9x,3y}. Then his indifference curves are? a. L-shaped curves. b. Smooth curves. c. Vertical lines. d. Horizontal lines. e. Straight lines that...

For the consumer, a point on an indifference curve that lies farther from the origin is preferable compared to those points that are closer to the origin. a. True. b. False.

Discuss the income and substitute effect of a price change according to indifference curve theory.

What is the significance of the indifference curve in microeconomics?

The standard assumption that economists make in consumer choice theory are: 1. More is preferred to less. 2. Consumers value a good relatively more if they have less of that good. 3. Consumers are...

Suppose a consumer is maximizing her utility, and then the consumer's income decreases. What will happen? a. The consumer will end up on a lower indifference curve than before. b. The consumer will...

A decreasing marginal rate of substitution indicates that an indifference curve is: a. a straight line. b. a vertical line. c. a horizontal line. d. bowed in, toward the origin.

The marginal rate of substitution increases as the consumer moves from left to right along a given indifference curve. True or false?

An indifference curve shows all combinations of two goods that: a) yield the same level of total utility to the consumer. b) yield no satisfaction to the consumer. c) cost the same amount of mone...

What does the slope of the indifference curve indicate?

Indifference curves: a. represent a set of product bundles to which a consumer is indifferent. b. slope up and to the right. c. show the difference between the marginal utilities of two different g...

Indifference curves cannot be concave to the origin because: a. consumers generally will prefer to have more of a good than less of a good. b. the satisfaction consumers get from consuming addition...

The effect is the change in the consumption of a good that would result if the consumer remained on the original indifference curve after the price of the good changes.

Which of the following is a true characteristic of an indifference curve map? \\ A. Moving northeast to a new indifference curve will increase utility. B. Indifference curves can cross.

Does a consumer well being vary along a demand curve? a. Yes. When price increases, consumers move to a lower indifference curve. b. Yes. When price increases, consumers move to a higher indiffer...

Why are indifference curves always down-sloping?

Clara consumes goods x and y. Her indifference curves are described by the formula y = \frac {k}{(x+5)}. Higher values of k correspond to better indifference curves. Which of the following is true?...

Sketch a graph of a continuous curve with the following properties

When would indifference curves be linear, vertical, or horizontal?

Why are indifference curves convex to the origin?

The table below shows the level of output a firm is capable of producing using different combinations of labor (L) and capital (K). Draw a graph plotting isoquants for the following levels of outpu...

Janelle and Brian each plan to spend $20,000 on a new car's styling and gas mileage features. They can choose all styling, all gas mileage, or some combination of two. Janelle does not care at all...

List and explain the properties of indifference curves.

What combination of X and Y will the consumer choose? Why?

Write the equation for the budget line LZ.

What is the price of X?

For the function, f(x) = x^3 - 12x + 2: a. Find the intervals of increase and decrease. b. Find the local maximum and minimum values. c. Find the intervals of concavity. (Concave up and concave dow...

Let the function f(x) = (x - 1)/(x^2) be given. a. Find the asymptotes of the function. b. Find the intervals on which the function is increasing and decreasing. Identify the function's local extre...

Sketch the graph of a function f(x) whose derivative f'(x) has the given description. f'(x) is negative on (1, 3) and positive everywhere else.

Sketch the graph of a function f(x) whose derivative f'(x) has the given description. f'(x) greater than 0 for x greater than 3 and f'(x) less than 0 for x less than 3

Answer the following questions for the function f(x) = xsqrt{x^2 + 4} defined on the interval (-7,5). a.) f(x) is concave down on the region {Blank}. b.) f(x) is concave up on the region {Blank}...

Find where the function f(x) = 3x^4 - 12x^3 - 168x^2 + 3 is increasing and where it is decreasing.

Sketch the graph of f ( x ) = x ( x 1 ) 2

For f ( x ) = x ( x 1 ) 2 Use the second derivative to find out where the graph is concave downward.

For f ( x ) = x ( x 1 ) 2 Use the first derivative to find out where the graph is increasing.

Sketch a curve with the following properties. f ( 0 and f "( 0 , for x( 3 f ( 0 and f ") 0 , for x ) 3

Consider the indifference curve budget line model of labor supply, and assume consumption and leisure are both normal goods. A higher wage rate would result in: a. more consumption and less leisure...

Consider f(x) = x^3 - 12x + 2. (a) Find the intervals on which f is increasing or decreasing. (b) Find the local maximum and minimum values of f. (c) Find the intervals of concavity and the inflect...

What is a budget constraint? How does a budget constrain explain consumer choices when used in conjunction with indifference curves?

A consumer has preferences over two goods: x and y. Three bundles, which all lie on the same indifference curve for this consumer, are shown in the following table.

Suppose that the consumer's preferences are described by the utility function U(x; y) = 5x + y, where y denotes the quantity of good Y and x denotes the quantity of good X that the consumer consume...

Use the second derivative to find the interval of concavity and the point of inflection for the following: y = xe^x.

a) What is John's long-run cost function? b) Suppose that John owns the regular shovel, and does not rent it anymore. What is the long-run cost function now?

Use the Monotonicity Theorem to determine where the given function is concave up and where it is concave down. F(x) = (x - 1)/(x^2).

1) Why do indifference curves have a negative slope? 2) What is a Giffen good?

Sketch the graph of the function that satisfies the given condition. f'(x) > 0 if 2 < mid x mid < 3.

You are offered two different sales jobs. The first company offers a straight commission of 9% of the sales. The second company offers a salary of $220 per week plus 4% of the sales. How much would...

Leo consumes only apples and bananas. He prefers more apples to fewer, but he gets tired of bananas. If he consumes fewer than 24 bananas per week, he thinks that 1 banana is a perfect substitute f...

In the hedonic pricing model of job risk, steep indifference curves indicate? A. a higher level of risk aversion. B. a lower level of risk aversion. C. that the cost of risk reduction is relatively...

Assume a consumer is currently purchasing a combination of goods, X and Y, that maximizes her utility given her budget constraint, i.e., MUx/MUy = PX/PY. Now assume that there is a decrease in the...

The consumer is choosing between two goods- good1 and good2. Good 1 is priced at $2 and good 2 is priced at $3. The consumer has a total of $600 to spend on both the goods. Let the utility functio...

Sketch the curve y = x*sqrt(4 - x^2), and determine the monotonicity and concavity of the curve.

1. If a consumer moves upward along an indifference curve, his or her total utility; A) remains constant. B) first decreases then increases. C) increases. D) first increases, then decreases. 2. The...

Consider the following function: f(x) = x^4 -32x + 3. Find the open intervals on which the function is increasing or decreasing.

Consider two goods, A and B. For each of the following scenarios, construct the utility function U(A, B) that matches the given information. a) The consumer believes that good A and B are perfect...

Which of the following is true of an indifference curve? a. Along an indifference curve utility is fixed. b. If a consumer is rational then indifference curves may cross. c. Indifference curves fur...

The marginal rate of substitution measures the distance between one indifference curve and the next one. (a) True (b) False.

Suppose all consumers are maximizing utility with convex indifference curves. All face the same prices and are perfectly rational. According to microeconomic models, at the maximization bundle, the...

Explain how to use indifference curve analysis in order to determine consumer equilibrium.

Find the values of x for which the given function is decreasing: y = 4x^3 - 3x^2 -36x - 6.

Find the values of x for which the given function is increasing: y = 4x^3 - 3x^2 -36x - 6.

Find the interval(s) in which the following function is decreasing: f(x) = x^3-27x + 7.

Indicate whether the statement is true or false. Explain your answer. Assume the market for corn is comprised of many buyers and sellers and resembles perfect competition. The use of corn to make e...

As long as a consumer remains on the same indifference curve? a. she is indifferent to all points which lie on any other indifference curve. b. her preferences will not affect the marginal rate o...

A consumer considers Coke and Pepsi to be perfect substitutes for each other. What would the consumer's indifference curves for these two goods look like? A) vertical along the entire length. B) up...

Why should the slope of a person's indifference curve equal the price ratio at their optimal choice? Explain this in terms of trade-offs. ( No graphs and an easy explanation.)

As a consumer moves rightward along an indifference curve,: a) the relative price of the good measured on the x-axis falls. b) the relative price of the good measured on the y-axis falls. c) the in...

Economists use indifference curves to characterize the preferences of a rational consumer. There are some plausible assumptions that lead to a set of 'well-behaved' (i.e., downward-sloping and stri...

Find the critical numbers and the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. y = x^3 - 3x + 8 STEP 1: Begin by finding the deri...

How does an increase in the price of a good affect the demand for its complement? How about its substitute? Give examples of goods that are complements. Give examples of goods that are substitutes.

Determine whether the following function contains a maximum value, minimum value, or both. Evaluate the function having maximum or minimum values at those points. Specify any points of inflection....

Label the following statement as True or False. A utility function is a functional representation of a consumer's indifference map. Each level of utility, corresponds to a unique indifference curve.

Prove that the function f(x) = 2x+sin x is increasing on all the linear.

A consumer considers Coke and Pepsi to be perfect substitutes for each other. What would the consumer's indifference curves for these two goods look like? a) L-shaped b) horizontal along its entire...

Find the intervals of increase and decrease for the function f(t) = 3t^5 - 5t^3 + 1.

For the function f(x) = x^3 + 6x^2 + 9x - 8, find the open intervals where the function is increasing or decreasing. Find all points where the function has extrema.

Consider the function: f(x) = x^2e^{2x}. The function has two inflection points at x = C and x = D, where in C is less than or equal to D. For the following interval, determine whether the functio...

Elvis only consumes Kraft dinners and steaks. One day, the price of Kraft dinners decreases, with no change in the price of steaks. a) Using a graph of indifference curves and budget constraints sh...

For the function f ( x ) = 2 x 3 + 6 x 2 18 x 130 , f(x) is decreasing on interval(s): _____

For the function f ( x ) = 2 x 3 + 6 x 2 18 x 130 , f(x) is increasing on interval(s): _____

Consider the equation below: f(x) = x^3 - 3x^2 - 9x + 9. Find the interval on which the function is decreasing.

Consider the equation below: f(x) = x^3 - 3x^2 - 9x + 9. Find the interval on which the function is increasing.

Consider the function below: f(x) = \dfrac{1}{2}x^4 - 4x^2 + 5. Sketch the graph of the given function.

Consider the function below: f(x) = \dfrac{1}{2}x^4 - 4x^2 + 5. Find the interval of decrease.

Consider butter and margarine, which are substitutes. When the price of butter falls, the demand curve for margarine is likely to: a) shift to the right. b) shift to the left. c) remain stationary....

Suppose that two goods, sprockets and trinkets, are substitutes. Other things equal, an increase in the price of sprockets will have which of the following effects in the market for trinkets? (a)...

What is a distinguishing characteristic of goods that are perfect complements? A) L-shaped indifference curves. B) Straight-line indifference curves. C) Curved indifference curves, bowed away from...

Given f(x) = 19x^{20} - 20x^{19} A. Find the interval(s) on which f is increasing. B. Find the interval(s) on which f is decreasing.

Suppose that f(x) = 2x^2 + 3x. (A) Find all critical values of f. (B) Use interval notation to indicate where f(x) is increasing or decreasing.

How to determine how a consumer divides their resources between two goods?

Good X is measured on the horizontal axis and good Y is measured on the vertical axis. The marginal rate of substitution is: A) the relative price of good X in terms of good Y. B) the relative pri...

Which one of the following is true at the best affordable choice of a consumer? A) Marginal rate of substitution is less than the relative price of the good measured on the r-axis. B) Other consu...

A consumer always has a cup of coffee with a tablespoon of sugar. What would the consumer's indifference curves for these two goods look like? a. L-shaped b. horizontal along the entire length c. d...

A consumer is at a corner solution - he buys meat, eggs, and vegetables, but no fish. a) The price of fish rises. Will this change his consumption of fish? b) The price of fish falls. Will this cha...

Determine whether the statement is true, false, or uncertain, and explain your reasoning. If apples (a good) are on the horizontal axis and dirty socks (a bad) are on the vertical axis then the ind...

Determine whether the statement is true, false, or uncertain, and explain your reasoning. If a consumer has preferences over two "bads" then these preferences cannot be convex.

Determine whether the statement is true, false, or uncertain, and explain your reasoning. If preferences are strictly convex, the set of points "no better than" any given point is a convex set.

Explain why the existence of diminishing marginal utility makes the indifference curve a curved line, not a straight line.

A consumer always has a cup of coffee with a tablespoon of sugar. What would the consumer's indifference curves for these two goods look like? A) downward sloping with a constant slope B) L-shape...

If A and B are complements in production and the price of A falls, the supply of B: a. increases and the price of B falls. b. increases and the price of B rises. c. decreases and the price of B fal...

i) What information does an indifference curve convey? ii) Why must a well-behaved indifference curve have a negative slope? iii) What are the two main implications of convex indifference curves?

At the best affordable point, which statement is true? a. The marginal rate of substitution between two goods equals their absolute price. b. Other points on the same indifference curve are afforda...

Which one of the following is true at the best affordable choice of a consumer? a) Marginal rate of substitution exceeds the slope of the budget line. b) Marginal rate of substitution is less than...

Which of the following statements is false? A) A consumer possesses a preference map. B) An indifference curve is a line that shows combinations of goods among which a consumer is indifferent. C...

Willy's friend, Wesley the Worker, is a school dropout. He has no daily personal commitments. Leisure is a normal good for Wesley. He has a positively-sloped supply curve of work hours. His MRSLI i...

What is a distinguishing characteristic of goods that are perfect complements? a. upward-sloping demand curves. b. curved indifference curves, bowed away from the origin. c. straight-line indiffere...

If the price of good X (measured on the horizontal axis) rises, the substitution effect is represented by a movement to a A) higher indifference curve. B) lower indifference curve. C) steeper part...

Describe each of the four properties of indifference curves.

Find out the intervals on which f(x) is increasing or decreasing, find out the local maximum and local minimum, and determine the concavity (concave up or down). f(x) = x^3 + 3x^2 - 3

The shape of a person's indifference curves between two goods depends on A) the prices of the two goods. B) the person's income. C) the degree of substitutability between the two goods. D) the l...

A consumer always has a cup of coffee with a tablespoon of sugar. What would the consumer's indifference curves for these two goods look like? a) downward sloping with a constant slope b) L-shaped...

Let f(x) = x^3 - 9x^2 + 24x. Find the interval(s) for which the graph of y = f(x) is decreasing.

Which one of the following statements is false? A) Indifference curves are bowed out from the origin. B) The marginal rate of substitution is the magnitude of the slope of an indifference curve....

Indifference curves for Perfect Substitutes are: a) upward sloping b) L-shaped c) linear d) vertical

Which of the following results in a rightward shift of your indifference curves for gasoline and movie rentals? A) an increase in the price of a liter of gasoline with no change in the price of a...

A consumer always has a cup of coffee with a tablespoon of sugar. What would the consumer's indifference curves for these two goods look like? A) L-shaped B) horizontal along the entire length C...

The slope of an indifference curve is _____, and a movement along the curve causes the loss in marginal utility (MU) of one good to _____ the marginal utility (MU) gained from another good.

The _____ is the absolute value of the slope of the indifference curve.

Determine intervals of concavity, and find inflection points of: f(x) = (\frac{x^2}{x^2+1})

You are given the following. f(x)= \dfrac{x^2}{x^2+3} On what interval(s) is f increasing?

Find the inflection points and the intervals of concavity for the function f(x) = 2x^3 + 5x - 1. Show your work.

What is the shape of an indifference curve?

Explain the relationship between the production contract curve and Pareto efficiency.

Explain the concept of an indifference curve.

Identify the shape of an indifference curve if two goods are perfect complements.

Identify the shape of the indifference curve if two goods are perfect substitutes.

i. A consumer has income of $3,000. Wine costs $3 per glass, and cheese costs $6 per pound. Draw the consumer's budget constraint with wine on the vertical axis. What is the slope of this budget co...

Maya divides her income between coffee and croissants (both of which are normal goods). An early frost in Brazil causes a large increase in the price of coffee in the United States. a. Show the ef...

Anya is awake for 100 hours per week. Using one diagram, show Anya's budget constraints if she earns $12 per hour, $16 per hour, and $20 per hour. Now draw indifference curves such that Anya's labo...

Pick a point on an indifference curve for wine and cheese and show the marginal rate of substitution. What does the marginal rate of substitution tell us?

Draw a budget constraint and indifference curves for pizza and Pepsi. - Show what happens to the budget constraint and the consumer's optimum when the price of pizza rises. - In your diagram, deco...

Draw a consumer s indifference curves for pizza and Pepsi. Explain the four properties of these indifference curves.

Compare the following two pairs of goods: - Coke and Pepsi - Skis and ski bindings \\ a. In which case are the two goods complements? In which case are they substitutes? b. In which case do...

Are film streaming services and movie tickets complements or substitutes? Explain.

Are film streaming services and TV screens complements or substitutes? Explain.

A college student has two options for meals: eating at the dining hall for $6 per meal, or eating a Cup O' Soup for $1.50 per meal. Her weekly food budget is $60. a. Draw the budget constraint show...

Sarah is awake for 100 hours per week. Using one diagram, show Sarah's budget constraints if she earns $6 per hour, $8 per hour, and $10 per hour. Now draw indifference curves such that Sarah s lab...

Draw the indifference curve for someone deciding how to allocate time between work and leisure. Suppose the wage increases. Is it possible that the person's consumption would fall? Discuss.

a.) Pick a point on an indifference curve for wine and cheese, and show the marginal rate of substitution. b.) What does the marginal rate of substitution tell us?

Draw a consumer's indifference curves for wine and cheese. Describe and explain the four properties of these indifference curves.

Compare the following two pairs of goods: 1.) Coke and Pepsi. 2.) Skis and ski bindings. a. In which case are the two goods complements? In which case are they substitutes? b. In which case...

At any point on an indifference curve, the slope of the curve measures the consumer's: a) income. b) willingness to trade one good for the other. c) perception of the two goods as substitutes or co...

Graphically illustrate and identify the features of an indifference curve.

Define an indifference curve. What is its slope?

A marginal rate of substitution of 2 means that, from the consumer 's point of view, 1 more unit of ______ is as good as 2 more units of ______.

Suppose Haya has $120 of income left each week after she pays her bills and puts some money away in a savings account, and she has two ways to spend this extra money: go to the movies, which costs...

An indifference curve consists of quantity combinations of two goods that yield _____.

An indifference curve has a negative slope because movement along the curve requires the consumer to give up the _____.

The marginal rate of substitution _____ as one moves downward along the indifference curve.

The slope of an indifference curve is equal to the ratio of the __________ of the good on the horizontal axis to the __________ of the good on the vertical axis. a. marginal utility (MU); marginal...

Draw the demand curves for the following goods. If the price of the first good listed rises what will happen to the demand for the second good, and why? a. hamburger and ketchup b. Coca-Cola and...

What are the three properties of indifference curves?

The top prize for the state lottery is $118,749,000. You have decided it is time for you to take a chance and purchase a ticket. Before you purchase the ticket, you must decide whether to choose th...

Find the interval where the function is increasing and the intervals where it is decreasing. f(x)=\frac1{x-2}

What are the goals of curve sketching? What can the first derivative of a function tell you about the original function? What aspects of a function's graph are described by the second derivative?

Explain why two indifference curves cannot intersect.

The demand for beer in Japan is given by the following equation: Q^{d} = 700-2P-P_{N} + 0.1I where P is the price of beer, P_{N} is the price of nuts, and I is average consumer income. What happ...

1. f(x) = -2x^2 + 20x - 10 2. f(x) = 2x^2 + 15x^2 - 180x + 72 3. f(x) = 6x^5 + 15x^4 + 10x^3 Find (A) intervals of increasing and decreasing (B) Internal of concavity (C) Relative maximum (D) Re...

What is the absolute value of the slope of the indifference curve? a. average rate of transitivity b. relative rate of utility c. marginal rate of transposition d. marginal rate of substitution

An indifference curve has a negative slope because movement along the curve requires the consumer to give up the: a. marginal utility of one good. b. total utility of one good. c. marginal substitu...

Consider the function f(x) = x^2 + 10x + 25/ x^2 +5 (a) Find critical values. (b) Find the intervals where the function is increasing and the intervals where the function is decreasing. (c) Use...

Acme Sales has two store locations. Store A has fixed costs of $125,000 per month and a variable cost ratio of 60%. Store B has fixed costs of $200,000 per month and a variable cost ratio of 30%. A...

Explain why indifference curves a. are downward sloping. b. are convex to the origin. c. do not cross.

What type of relationship would you expect between sales of hot dogs and sales of hot dog buns?

Consider the markets for film streaming services, TV screens, and tickets at movie theaters. a. For each pair, identify whether they are complements or substitutes. b. Suppose a technological advan...

An indifference curve consists of quantity combinations of two goods that yield: a. equal marginal utilities. b. the same price ratios. c. the same total satisfaction. d. negative marginal utilities.

The slope of an indifference curve is equal to the ratio of the of the good on the horizontal axis to the of the good on the vertical axis. a. marginal utility (MU); marginal utility (MU) b. total...

Consumers always indifference curves that are farther from the origin. a. reject b. cross c. prefer d. maximize

The is the absolute value of the slope of the indifference curve. a. marginal rate of substitution b. average rate of transitivity c. relative rate of utility d. marginal rate of transposition

The slope of an indifference curve is, and a movement along the curve causes the loss in marginal utility (MU) of one good to the marginal utility (MU) gained from another good. a. zero; maximize b...

Suppose we have f(x) = 3x^4 -16x^3 + 24x^2. a. Find all critical points of f(x). b. Make a table showing the intervals on which the graph of f(x) is increasing or decreasing. c. Use the first deriv...

What is the shape of the indifference curve if the law of diminishing marginal utility did not hold?

What is the shape of the indifference curve, if MRS was zero and constant?

Explain why indifference curves are downward sloping, are convex to the origin, and do not cross.

Describe the shape of an indifference curve.

In a perfectly competitive market, the demand curve for labor a. slopes upward. b. slopes downward because of diminishing marginal productivity. c. is perfectly elastic at the equilibrium wage rate...

Assume the price of good X is Px, the price of good Y is Py, and B is the budget. The formula for the budget line for these two goods is: a. PyQy/PxQx b. PyB + PyB = B c. PxX + PyY = B d. (1 - Py/B...

Which of the following is true concerning an indifference map? a. Each consumer has a map of indifference curves. b. Consumers always prefer curves farther from the origin. c. Each indifference cur...

The slope of the indifference curve for goods X and Y is called the marginal a. product rate. b. rate of transformation. c. rate of substitution. d. rate of utility.

Assuming steak and potatoes are complements, a decrease in the price of steak will: a. decrease the demand for steak. b. increase the demand for steak. c. increase the demand for potatoes. d. decre...

Graphically illustrate and explain the features of an indifference curve.

For the function f(x) = \frac{1}{x^{2} + 3}, indicate where the function is increasing or decreasing, where any relative extrema occur, where any asymptotes occur, where the graph is concave up or...

Sketch the graph of the given function by determining the appropriate information and points from the first and second derivatives. y= x^3 - 6 x^2 - 63 x

Consider the function f(x) = 3x^{4} - 4x^{3} . (1) Find the intervals over which the function f(x) is increasing and the intervals on which it is decreasing. (2) Find the intervals over which th...

Find the largest open interval where the function is changing as requested. Where f ( x ) = 1 4 x 2 1 2 x is increasing. A. (-1,1) B. ( , ) C. ( , 1 ) D. ( 1 , )

Please answer to the question below Consider the Function below. f ( x ) = 4 + 3 x x 3 (a) Find the interval of Increase using interval notation. (b) Find the interval of decrease using interval...

Suppose that 2 x x 2 4 (a) Use interval notation to indicate where f ( x ) is decreasing. (b) Find all vertical asymptotes of f . (If there are no vertical asymptotes, specify)

Find all critical points of f(x) = -x^4 + 8x^3 - 16x^2 + 32 and classify each as a relative minimum, relative maximum, or neither one.

Sketch an isoquant that represents the inputs that are perfect complements, using 1X with 2Y inputs.

f(x) = 3x4 - 4x3 -12x2 + 5 (a) Determine the intervals on which f is increasing and the intervals on which f is decreasing. (b) Find all local extrema of f and use the first derivative test to dete...

The price of wine has risen from $5 to $10 per bottle and the price of cheese has fallen from $10 to $5 per pound, while Jackie's income has stayed fixed at $50 per week. Is it possible for Jackie...

A. If the prices of all products are rising at 5 percent per year and your employer gives you a 5 percent salary increase, are you better off, worse off, or equally well off in comparison with your...

Assume that compact discs and compact disc players are complements. When the price of compact disc players decreases: A) the demand for compact discs increases. B) the demand for compact discs de...

Within the relevant range, isoquants A) are negatively sloped B) are convex to the origin C) cannot cross D) All of the above

Suppose the function f(x) has a domain of all real numbers and its derivative is shown below. f'(x) = (x + 4)^{5}(x - 8)^{4}e^{(x - 11)} Find the intervals where f(x) is increasing. (Write your ans...

For the following function, f(x) = 5 - 4x - 9x^{2} - 3x^{3} (i) Identify the critical points of the function; (ii) Determine the open intervals where the function increases and decreases; (iii) Cla...

On the R-S model utility is found A) on the vertical axis B) nowhere C) from indifference curves that can be traced on the graph itself D) on the horizontal axis E) none of the above

Given f(x) = x^3 - 12x^2 + 36x: (A) Find the intervals where the function is increasing/decreasing. (B) Find the ordered pairs for all local extrema. (C) Find the intervals where the function is co...

Consider the function f(x) = sin^2 x + sin x on the interval (0, 2 pi). Find the open intervals on which the function is increasing or decreasing.

Consider the function f(x) = sin^2 x + sin x on the interval (0, 2 pi). Apply the First Derivative Test to identify all relative extrema of the function.

Consider the function f(x) = cos^2 (2x) on the interval (0, 2 pi). Find the open intervals on which the function is increasing or decreasing.

Consider the function f(x) = sin x cos x + 5 on the interval (0, 2 pi). Apply the First Derivative Test to identify all relative extrema of the function.

Apply the First Derivative Test to identify all relative extrema of the function f(x) = (x^2 - 2x + 1)/(x + 1).

Apply the First Derivative Test to identify all relative extrema of the function f(x) = x^2/(x^2 - 9).

Find the open intervals on which the function f(x) = sin^2 x + sin x, 0 less than x less than 2 pi is increasing or decreasing.

Tasty Treats plans to open a new retail store in Medina, Ohio. Tasty Treats will sell specializing cupcakes for $5 per cup cake.(Each cupcake has a variable cost of $2). The company is negotiating...

Suppose Nancy enjoys movies and books, and her preferences are represented by the utility function 3X + 7Y, where X is movies, and Y is books. Her marginal utility of movies is 3 and her marginal u...

Assuming product X and Y are normal, draw a demand curve for product Y, using the indifference curve and budget line. Show all your work and provide an explanation.

Analyze and sketch graph of the function f ( x ) = x 3 + x + 4 x . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.

Peter also likes coffee (x) with sugar (y), but his utility function is U(x, y) = 5x + 4y. Peter has purchased 4 ounces of coffee and 5 grams of sugar. Assume that Peter has $9 to spend on coffee a...

Petra consumes only two goods, pizza (P) and hamburgers (H) and considers them to be perfect substitutes, as shown by his utility function: U(P, H) = P + 4H. The price of pizza is $3 and the price...

A curve that represents all combinations of market baskets that provide the same level of utility to a consumer is called: A) budget line B) isoquant C) indifference curve D) demand curve

The income-consumption curve illustrates: A) combinations of incomes needed with various levels of consumption of a good B) the income-demand curve C) the utility-maximizing combinations of goods a...

Why are indiffernce curves convex? A) the substitution effect is negative B) the marginal rate of substitution is diminishing C) if the income effect is negative D) the marginal rate of substitutio...

The assumption of transitive preferences implies that indifference curves must: A) not cross one another B) have a positive slope C) be L-shaped D) be convex to the origin

Find all relative extrema of the function. f(x) = 2x - 24x^{\frac{1}{3}} Relative maximum (x,y) = \boxed{\space} Relative minimum (x,y) = \boxed{\space}

Let the function f(x) = 1 +(7/x) - (6/x^2). (a) Find the interval where the function is concave up. (Enter your answer using interval notation.) (b) Find the interval where the function is concave...

f(x) = (4x^2) / ((x^2) + 4) (a) What are the critical numbers of the function? (b) Where is the function increasing and decreasing in interval notation? (c) What are the x-coordinates of all local...

Provide examples on how the availability of close substitutes affects price elasticity of demand for a good or service.

Suppose that the State of Washington (that is, the median voter in Washington) has the following preferences of Education E and other goods G: U(G;E) = lnG + (1 - a ) lnE The price of education is...

Consider the function f(x) = x^4 - x^2. a) Find the intervals where f(x) is increasing and the intervals where f(x) is decreasing. b) Find the intervals where f(x) is concave up and the intervals...

Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.) y = \frac{x}{(x^2 + 4)} Points of...

The table below describes the number of cars and TVs a worker can produce (MPL) in the US and Mexico. The US and Mexico both have 40 workers. Suppose that without trade, the US consumes 60 cars and...

For the function \displaystyle f(x) = \frac{x}{2}+\cos x on the interval (0, 2\pi), (a) Find the open intervals on which the function is increasing or decreasing (b) Apply the First Derivative Test...

When two goods are perfect substitutes their indifference curves are (blank) and the marginal rate of substitution (blank). a. L shaped curves; diminishes quickly b. Straight lines; is constant c....

Consider the following function: f(x)=x^{4}e^{-x} a.) find intervals on which f is decreasing or increasing b.) find local maximum and minimum values c.) find intervals of concavity and inflec...

If an indifference curve is convex (bowed outward), which of the following statements would be true? a. The more you have of a good, the less you desire additional units of the good. b. The less yo...

The slope of an indifference curve shows: a) The change in utility from an additional unit of the good. b) The rate at which the consumer is able to substitute one good in the market. c) Is equal t...

Let f(x) = 8x + \frac{6}{x} (A) Use interval notation to indicate where f(x) is increasing. Increasing:\boxed{\space}.(B) Use interval notation to indicate where f(x) is decreasing. Decreasing: \...

Determine the annual unit volume at which Paper Mate is indifferent between the two manufacturing methods.

Given f(x) = x^2 - 5x, find 1. Interval where f is increasing or decreasing. 2. Local minima and maxima of f. 3. Interval where f is concave up or concave down. 4. The inflection points of f, and...

Suppose the consumer's indifference curves are concave (i.e., bowed away from the origin) instead of convex. In this situation, A. along an indifference curve, the marginal value of X is falling...

Suppose Timothy consumes two goods, soda and chips. The slope of his indifference curve for these two goods reflects: \\ A. the rate at which he is willing to substitute one good for the other. B....

If a consumer's income increases, that consumer's budget constraint: a. shifts inward toward the origin. b. does not change. c. pivots on the vertical axis. d. shifts outward away from the origin.

When a consumer optimizes his/her satisfaction at a point at which an indifference curve is tangent to the budget constraint: a. the consumer can increase his/her satisfaction only by increasing hi...

An indifference curve is a set of points representing combinations of goods that a consumer finds desirable and satisfying. a. three; unequally b. three; equally c. two; unequally d. two; equally

True or false? An indifference curve that lies tangent to the budget constraint illustrates the combination of goods X and Y that provides the consumer with the least satisfaction.

Let f(x) = x^3 + 7.5 x^2 - 18x - 1. a. Find f'(x) and f''(x). b. Determine the intervals where f is increasing or decreasing. c. Find all relative maxima and minima. d. Find the intervals where f i...

Consider the function f(x) = 5x^3-30x. On a separate sheet of paper, graph the function. Mark on your graph the intervals where the function is increasing/decreasing and the points at which the fun...

Pneu Shoe Company manufactures various types of athletic shoes. Several types require a built-in air pump. Presently, the company makes all air pumps it requires. However, management is evaluating...

What is the slope of an indifference curve?

What is an example of complementary goods?

A student is first and foremost interested in beer and would be willing to forgo any quantity of milk for the smallest additional quantity of beer. However, if the beer consumption is given, the st...

Every evening, Lena drinks tea (t) or coffee (c). She is indifferent between the two and hence, her preferences can be represented by the utility function U(t, c) = t + c. The price of a cup of tea...

Vista Company manufactures electronic equipment. In 2015, it purchased from an outside supplier the special switches used in each of its products. The supplier charged Vista $2.20 per switch. As an...

Sketch the graph of the following function, indicating intercepts, asymptotes, where it increases, where it decreases, any relative maximum and relative minimum points, where it is concave upward,...

Use the first derivative test to locate the relative extrema of the function in the given domain, and determine the intervals of increase and decrease. g(t) = 8e^(-t^2) with domain (-infinity, +in...

Suppose that the first and second derivatives of a function y = f(x) are given by: f'(x) = xe^x\ and\ f"(x) = e^x(x + 1). Which statement is true? a. f(x) is increasing and opens down on (-1, \inft...

U(X, Y ) = XY + 10Y a) Find the marginal rate of substitution, b) discuss how MRS XY changes as the consumer substitutes X for Y along an indifference curve, c) derive the equation f...

Homer consumes only donuts and beer. When he consumes less than 10 beers, Homer would gladly drink one more. After drinking 10 beers, Homer is so drunk that he does not notice any additional bottle...

Raymond's preferences are represented by the utility function U(x, y) = x/y if y greater than 0 and U(x, y) = 0 if y = 0. Why Raymond has indifference curves that are upward- sloping straight lines...

Oswald Odd consumes only goods 1 and 2. His utility function is U(x1, x2) = x1 + x2 + min{x1, x2}. What dose Oswald's indifference curve looks like?

Suppose the utility function is U(x, y) = min(x, y) Determine the substitution and income effect of a change in the price of x, and what is the demand equation for x?

Consider a worker (Ann) who gets utility from consumption c and leisure l. Ann chooses how many hours each day to supply to the labor market where h = 16 - l subject to the market hourly wage w = 1...

In preparing for a party you ask your friend what snacks and wines he would like you to buy. His answer is that he prefers California Red Wine and pretzels to California White Wine and pretzels; an...

Determine the open intervals on which the graph of the function is concave upward or concave downward. y = x + \dfrac {2}{\sin x}, \ (- \pi, \ \pi)

Assume that the budget constraint shown is for $600 of income with a price of food equal to $2 and a price of clothes equal to $4. With an indifference curve and budget constraint as shown, will a...

Given a consumer's preferences are rational and well-behaved, how do I know the consumer's indifference curve must be downward sloping?

Consider the function f(x) = 2x/x^2 - 1 (a) What are the zeros (root) f the function. (b) On what interval is the function is increasing and decreasing? (c) What are the local maxima and minima?

For the function f(x) = 4x - 1/3 x^2 - 10 (a) Find and classify all local extrema, on what interval is f(x) is increasing and decreasing? (b) Find all points of infection on what interval is f(x) i...

Consider two utility functions, U(c1, c2) and V(c1, c2) that satisfy V(c1, c2) = 5U(c1, c2). Show that the indifference curve maps of U and V are identical. Suppose 5 is replaced by any positive nu...

Consider the function f(x) = x2e14x. (a) For this function there are three important intervals: (-infty, A), (A, B), and (B, infty) where A and B are the critical numbers. Find A and B. (b) For eac...

Find the critical numbers and the open intervals on which the function is increasing or decreasing. y = -3(8x - 7)^4

Find the critical numbers and the open intervals on which the function is increasing or decreasing. g(x) = 2(5x - 1)^3

Find the critical numbers and the open intervals on which the function is increasing or decreasing. g(x) = (x + 2)^2

Find the critical numbers and the open intervals on which the function is increasing or decreasing. f(x) = \frac 14 x^4 - \frac 13 x^3 - x^2

Find the critical numbers and the open intervals on which the function is increasing or decreasing. y = 3x^3 + 12x^2 + 15x

Find the critical numbers and the open intervals on which the function is increasing or decreasing. y = x^2 - 6x

If Sam's preferences relating her own income and Oscar's income conform to the Golden Rule ( Love thy neighbor as thyself"), what would her indifference curves look like?

Consider a couple's decision about how many children to have. Assume also that over a lifetime, a couple has 325000 hours of time to either work or raise children. The wage is $10 per hour. Raising...

Given: f(x) = (3x-4)/(x+6) (a) Use interval notation to indicate where f(x) is increasing or decreasing. (b)Find the x-coordinates of all local maxima and minima of f. (c) Use interval notation to...

Analyze and sketch a graph of the following function, label any intercepts, relative extreme, points of inflection and asymptote. Use a graph utility to verify your results. y = x 4 x

You are offered a five year lease at a fixed cost of $42,000 per year or a variable lease rate equal to 10% of revenue. Sales are projected to be $505,000. Find the indifference point and determine...

Consider the equation below. (If an answer does not exist, enter DNE.) f(x)=x^3-12x^2-27x+2 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.)

The cost structure of two firms competing in the same industry is represented by the following cost formulas: Company X = $2,401,000 + $52/unit Company Z = $1,076,000 + $102/unit The selling price...

Consider the function below. f(x) = 1 + 2x^2 - x^4. (a) Find the interval of increase and the interval of decrease. (Enter your answer using interval notation.) (b) Find the local minimum value(s...

Do the detailed graphing for f(x) = \frac{(x + 1)^2}{1 + x^2}. a) The intercepts ( x and y intercept) b) The asymptotes (vertical and horizontal) c) Critical points d) Interval on which the...

Given y = \frac{4}{x - 1}. Determine the following and sketch the graph. a) domain b) x- and y-intercepts c) horizontal and vertical asymptotes d) intervals where the function is increasing/decreas...

Given y = x^4 - 4x. Determine the following and sketch the graph. a) domain b) x- and y-intercepts c) horizontal and vertical asymptotes d) intervals where the function is increasing/decreasing e)...

Assume that an individual's preferences is represented by the utility function U(x, y) = 5x + 2y. A. What could you tell about the type of x and y? Good, bad, or neutral? B. Derive the equation for...

1) a) Graph the function f(x) = x^5 - 5x^3. b) Use the first derivative test to find the location of all local extrema for f(x). c) Use the second derivative test to find the location of all local...

Consider the function: f(x) = 2x/x^2-1 Find the following: (a) Where are the zeros (roots) of this function? (b) Where are the local minimum and maxima? (c) What are the infection points?

Determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph, showing as many key features as possible (high and low...

With the per-unit prices of broccoli (B) and pork rinds (R) equal to $2 and $1, a consumer, George, with an income of $1,000 purchases 400R and 300B. At that point, the consumer's MRS_BR = 2R/1B. D...

Find the critical points of the function f(t) = \frac 15 t^5 - a^4 t. Assume a is a nonzero constant.

Find the critical points of the function f(x) = 12x^5 - 20x^3.

Given the function f(x) = 2x^3 - 6x on the domain [-4, 4] a) What are the x- and y-intercepts of the function? b) What is/are the relative maximum and maxima point(s) of this function? Include a si...

Refer to a hypothetical social drinker, Carlota, who goes to a pub every evening. It Is assumed that she is

Let f(x) = x(x - 3)^2. a. Find the first derivative of f. b. Find the second derivative of f. c. Analyze f', f", f and summarize your analysis in a table. d. Sketch the graph of y = f(x). Mark the...

Let f(x) = 6x^3 - 15x^2 + 12x a) Find the open intervals on which the function f(x) is increasing or decreasing. b) Use the First Derivative Test to find all ideal max and minimum values of functio...

Sketch a graph of a single function that has these properties. Continuous and differentiable for all real numbers f'(x) less than 0\; \text{on}\; (-\infty, -3)\; \text{and}\; (0, \infty)\\ f'(x) gr...

Consider the following: x = t^3 - 12t \\ y = t^2 - 1 (a) Find the following. \frac{dy}{dx} = \boxed{\space}.\\\frac{d^2y}{dx^2} = \boxed{\space}. (b) For which values of t is the curve concave upw...

Translate the characteristic into a statement about the graph of the function. f''(x) greater than 0\; \text{on}\; (\infty, 0) Then, sketch the graph of a function, f that satisfies the given chara...

Translate the characteristic into a statement about the graph of the function. f''(0) = 0 Then, sketch the graph of a function, f that satisfies the given characteristic.

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