1) Let f(x) = \frac{x - 8}{x + 4}. Find the open intervals on which the function is increasing...
Question:
1) Let {eq}f(x) = \frac{x - 8}{x + 4} {/eq}.
Find the open intervals on which the function is increasing (decreasing). Then determine the coordinates of all relative maxima (minima).
{eq}f {/eq} is increasing on the intervals _____
2) Find the critical point and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to the critical point. Let {eq}f(x) = - \frac{4}{x^2 + 4} {/eq}
The interval on the left of the critical point is _____
The interval on the right of the critical point is _____
3) The moose population on a small island is observed to be given by the function {eq}P(t) = 120t - .4t^4 + 700 {/eq} where {eq}t {/eq} is the time (in months) since observations of the island began.
The maximum population is {eq}P(t) = {/eq} _____ moose
When does the moose population disappear from the island? {eq}t = {/eq} _____
Min Max Problem
This problem is based on the application of the concept the derivatives. When it comes to the critical point we know that the critical point of a function is the point at which the derivative of a function is either undefined or is zero. The critical point helps us define the intervals of monotone and thus, we are able to define the points of maximum and minimum.
Answer and Explanation: 1
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Part 1:
We have,
{eq}f(x) = \frac{(x-8)}{(x-4)} {/eq}
Let us calculate the derivative. Using the quotient rule, we get,
{eq}f'(x)=\frac{12}{(x...
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Maximum & Minimum of a Function | Solution & Examples
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Chapter 15 / Lesson 1
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Understand how to find the local max and min of a function. Discover how to identify maximum and minimum points of a function. See examples of local maximum and minimum to better learn how to solve min-max problems.
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