Sketch the graph of the function. Label on the graph the coordinates of any relative extrema,...
Question:
Sketch the graph of the function. Label on the graph the coordinates of any relative extrema, points of inflection, asymptotes, intercepts.
{eq}f(x) = \frac{x^2 - 6x + 12}{x - 4} {/eq}
Inflection Points and Asymptotes:
It is important to know which are the inflection points where a change in the concavity of the function occurs.
In the same sense, if the function does not have inflection points, this does not mean that its concavity does not change.
That is, the concavity change can occur at points where the function is not defined as in a vertical asymptote.
Answer and Explanation:
Become a Study.com member to unlock this answer! Create your account
View this answerThe function is:
{eq}f(x) = \frac{x^2 - 6x + 12}{x - 4} \\ {/eq}
Relative Extreme
We classify the critical points of a function in relative...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
from
Chapter 8 / Lesson 14Learn what optimization means in calculus. Discover the optimization problems. Learn the steps to solve the optimization problems. See optimization problem examples.
Related to this Question
- Analyze and sketch the graph of y = {2 x^2 - 5 x + 5} / {x - 2}. Find and label any intercepts, relative extrema, points of inflection, and asymptotes. Graph the function.
- Analyze and sketch the graph of the function, f(x) = e^{3x} (2 -x), label the intercepts, relative extrema, point of inflection, and asymptotes.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. y = x^2 - 10x + 65 x - 8
- Analyze and sketch the graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. y = -x^2 - 2 x + 3
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. f(x) = x^4-4x^3+16
- Analyze and sketch a graph of the function: y = (x^2)/(x^2 + 3). Label any intercepts, relative extrema, points of inflection and asymptotes.
- Sketch the graph of the following: f(x) = x^{5/3} - 5x^{2/3}. Label the following: domain, relative extrema, points of inflection, asymptotes and intercepts.
- Sketch the graph if y=x^4+4x^3 Label on the graph all extrema and inflection points.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = \frac{x^2 - 6x + 12}{x - 4}
- Give a graph of the polynomial and label the coordinates of the intercepts, stationary points, and inflection points. f x = 2- x + 2x^2 - x^3
- Analyze and sketch a graph of the function. Find any intercepts, relative extrema,points of inflection and asymptotes. f(x) = \frac{x^3}{x^2-81} Intercept \hspace{20mm} (x,y) = ( \rule{20mm}{.5pt
- Sketch the graph f (x)= 2{(x^2) - 9} / {x^2 - 4} include intercepts, asymptotes, extrema and points of inflection.
- Sketch the graph of the given function. Label the intercepts, relative extrema, points of inflection, and asymptotes, if any. (more space next page) f(x)=\frac{x}{\sqrt{x^{2}+7
- Give a graph of the polynomial and label the coordinates of the intercepts, stationary points, and inflection points. f x = 2x^3 - 3x^2 - 36x + 5
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f (x) = (x + 1)(x - 2)(x - 5)
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. g(x)=x\sqrt{9-x^2}
- 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.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y=\frac{2x^2-5x+5}{x-2}
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. h(x)=x\sqrt{4-x^2}
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. g(x)=x\sqrt{9-x}
- Analyze and sketch graph of the function f ( x ) = ( x 3 ) ( x + 2 ) 3 . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = -1 / 3 (x^3 - 3 x + 2)
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. g(x)=x-\frac{8}{x^2}
- Analyze and sketch graph of the function f ( x ) = 4 x x 2 . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = 1 / {x - 2} - 3
- Analyze and sketch graph of the function f ( x ) = 5 3 x x 2 . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y=x^5-5x
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x)=\frac{x-3}{x}
- Analyze and sketch graph of the function f ( x ) = x 1 / 3 ( x + 3 ) 2 / 3 . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f (x) = x^3 / x^2 - 9
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y=\frac{x^2+1}{x^2-4}
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = 3 x^4 - 6 x^2 + 5 / 3
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = |x^2 - 6 x + 5|
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = 3 (x - 1)^{2/3} - (x -1)^2
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = x / {x^2 + 1}
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) = x^4 -8x^3 + 18x^2- 16x + 5
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y=x\sqrt{4-x}
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f (x) = 1 / 3 (x - 1)^3 + 2
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = 2 - x - x^3
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y=\frac{3x}{x^2-1}
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = (x - 1)^5
- Analyze and sketch graph of the function f ( x ) = 2 x 1 + x 2 . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = 3 x^4 + 4 x^3
- Analyze and sketch graph of the function f ( x ) = x 4 2 x 2 + 6 . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Analyze and sketch a graph if the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.\\ y= \frac{x^2-6x+12}{x-4}
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f (x) = x + 32 / x^2
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f (x) = 3 x^3 - 9 x + 1
- Analyze and sketch graph of the function f ( x ) = ( x 2 4 ) 2 . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f (x) = x^2 + 1 / x
- Analyze and sketch graph of the function f ( x ) = x 2 + 1 x . Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = x^2 / x^2 + 3
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = x^3 - 3 x^2 + 3
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y = |2 x - 3|
- Analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. y=3x^{2/3}-2x
- Sketch the graph of the polynomial function f(x)=3x^4-4x^3-12x^2? Label the axes, intercepts and x- and y- coordinates of the turning points.
- Sketch the graph of a function that satisfies: f'(x) 0 \\f''(x) 0 if x 2 and f''(x) 0 if x 2 , f has inflection point (2,5). \lim_{ x \to \infty} f(x) = 8 and \lim_{x \to \infty} f(x) = 0 .
- Sketch the graph of the given function with their inflection points. y = cos t with an inflection point at t = pi/2
- Analyze and sketch graph of the function f(x) = x square root(16 - x^2). Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.
- Sketch the graph of the given function with their inflection points. y = 500/(1 + 24e(-0.26t)) with an inflection points at t = 12.2.
- Sketch the graph of the given function with their inflection points. y = exp (-t2) with an inflection points at t = -0.7 and 0.7
- Sketch the graph of the given function with their inflection points. y = te-t with an inflection points at t = 2
- Graph f(x)=\frac{x}{(2x-3)^2}. Label in the graph any points of inflection.
- Given a function f(x)2/3x^3+5/2x^2-3x. a) Find i. The inflection point. ii. The y-intercept and x-intercept. b) Sketch the graph of f(x).
- y=x^3-4x^2+6 Sketch the graph of the function. Label any intercept, relative extreme, points of inflection, and asymptotic. I'm having a hard time factoring the cubic polynomial. I think the polynomial is incomplete.
- Given a function f(x) = (2/3)x^3 + (5/2)x^2 - 3x. A) Find the inflection point. B) Find the y-intercept and x-intercept. C) Sketch the graph of f(x).
- For the curve given by the equation y = x^3 + fraction {3}{2} x^2 - 6x Sketch the graph, labeling the relative maxima (MAX), relative minima (MIN) and points of inflection (POI). Describe where the c
- The graph of f "(x) is shown. Use the graph to find the values of x that will give inflection points for the function f(x).
- Using the graph of g ' in the figure below and the fact that g(0) = 50, sketch the graph of g(x). Give the coordinates of all critical points and inflection points of g.
- Sketch the graph of the function f(x) = -x^2 - 2x - 1 . Indicate the x- and y- intercepts. Indicate any extrema.
- Draw a complete graph the following functions, finding all critical points and labeling on the graph. Find and label the asymptote lines: 1. f(x) = 2^{x-1} - 2 2. f(x) = e^{-x}
- Analyze and sketch a graph of y = 6 x^2 /3 + 2 x. Label any intercepts, relative extrema, and points of inflection. Use a graphing utility to verify your results.
- 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
- Analyze and sketch a graph of the function, label any intercepts, relative extreme, points of inflection and asymptote. use a graph utility to verify your results. y = x 2 4 x 7 x + 3
- Sketch the graph of a function that satisfies the following. f'(-2)=f'(2)=0; f'(x) 0 { for } |x| 2; f'(x) 0 { if } 2 x 4; f''(x) 0 { for } xin(-4,0); f'(x)=0 { for } x 4; f { has an inflection point a
- a) Sketch the graph of f(x) = (1 - x)/((x^{2}). Identify all intercepts, relative extrema, points of inflection, and asymptotes. b) A rocket that is launched vertically is tracked by a radar statio
- The graph of y= f'(x) is shown below. Give the largest value of x where the graph of f(x) has a point of inflection.
- The graph of y = g(x) is shown in the figure above. Label the following points on the curve. A. Point A is a point on the curve where the derivative is negative. B. Point B is a point on the curve where the value of the function is negative. C. Point C is
- Sketch the graph of the following function. State where any intercepts occur, where asymptotes occur, where any relative extrema occur, where the function is increasing or decreasing, where any inflec
- Sketch the graph of the given function with their inflection points. y = sin x with an inflection point at t = pi
- Sketch the graph of the polynomial function P(x) = -2x(x-2)^2 . Label the intercepts.
- Sketch a possible graph of a function y=f(x) over the interval [-2,2] when its derivatives have the following properties: a. f'(x)=0 for x=1 and x=-1, f'(x) 0 for x in (-2,-1) and f'(x) 0 for x in (-1,1) and (1,2) b. f''(x)=0 for x=0 and x=1, f''(x) 0 f
- Use a graphing utility to graph f and f' over the given interval: f(x)=x^3-1.9x^2-0.99x+1.45; parentheses -2,2 parentheses\\ Determine any points at which the graph of f has horizontal tangents.
- Sketch the graph of the equation. Label the vertex and the intercepts. y = -x^2 + 8 x - 16
- Given the function f(x) = x^2 - 2x, determine the equation of the tangent to f(x) at x = 3. Draw a clean graph, label your axes, and indicate the coordinates (x, y) of your intercepts as well as the p
- Graph the following functions. Plot and label at least 3 points for each graph. a.\ f(x) = \log_3(x)\\ b.\ f(x) = \log_{\frac{1}{2 (x)\\ c.\ f(x) = \log_2 (x + 3)\\ d.\ f(x) = 1 + \log_2(x)
- Sketch the graph of f ( x ) = e^x making sure to label all x and y intercepts, maximums, minimums, and inflections points.
- The figure below is the graph of the derivative f' of a function f. a) Give the x-coordinate(s) of the inflection point(s) of f. b) If there is more than one inflection point, enter them as a comma
- The graph of a function f(x) is given below. Sketch a graph of f'(x) on the interval from -5 to 5.
- Use the graph of y = f(x) to sketch a graph of the derivative function f?(x).
- Sketch graph of a function f(x,y)=\begin {cases}1 &if\, y is greater than 0 \,and\, y is less x^6 \\ 0 &otherwise. \end {cases}. And sketch the graph od z=f(x,y).
- sketch a graph of function f(x)=10x^6-36x^5-75x^4+300x^3+120x^2-720x. identify local extreme, inflection points, and __x__ and __y__ intercepts.
- Consider the quadratic function f, given by f ( x ) = x 2 + 6 x + 8 Sketch a graph of y = x 2 + 6 x + 8 clearly labeling the vertex of the parabola, along with any intercepts with the x- and y-axes.
- Sketch the graph of the quadratic function f(x) = -2x^2 + 6x-3. On the graph, show the value of x and y intercepts, vertex, and axis of the quadratic function. Give the domain and range of the function also.
- (a) Sketch the graph of the function y = x^2. (b) Sketch the graph of the function y = (x + 1)^2. (c) Sketch the graph of the function y = (x + 1)^2 - 3. (d) Give the coordinates of the vertex of the parabola from part (c). (e) Convert the vertex form fro
- Sketch the following curves, indicating all intercepts, relative extreme points and inflection points. y = x^3-6x^2+9x
- 1. Sketch the graph of the function f(x) = \begin{cases} x + 3 & \text{ if } x < 5\\ 5 & \text{ if } 0 \leq x \leq 5 \\ x^2 - 1 & \text{ if } x < 0 \end{cases} 2. Use the graph of f(x) to answer the following questions: a. \lim_{x \to 5} f(x) = ? b. \
- For f(x) = 12 + 2x^2 - x^4. Determine the following. \\ A. Inflection points(s). B. Sketch the graph of y = f(x).
- Use the graph of the function y = f(x) shown in the given figure. Determine the x-intercepts of the derivative y = f'(x).
- If the graph of y = ax #x00b3; + 4x #x00b2; + cx + d has a point of inflection at (1, 0), then the value of a is a) -4/3 b) -2/3 c) 2 d) 0 e) 1/2
- Sketch the graph of the following function, showing intercepts and all stationary points: f(x) = x^3 - 2x^2 - 8x.