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Q. 20

Expert-verified

Found in: Page 260

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Find the possibility graph of its derivative f'.

The possibility graph of its derivative f' is

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given

The given information is

Step 2. Explanation

The objective is to sketch a possible graph of its derivative f".

From the above graph, the function f(x) is increasing in the interval (-3.2,-2.2) and

(-1,1.5)

So. f'(x) > 0 is in the interval (-3.2,-2.2) and (-1,1.5)

From the above graph, the function f(x) is decreasing in the interval (-2.2,-1) and

(1.5,2.1)

f'(x) < 0 in the interval (-2.2,-1) and (1.5,2.1)

f'(x)=0 at x = -2.2, x=-1 and x = 1.5.

Most popular questions for Math Textbooks

Determine whether or not each function f in Exercises 53–60 satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b]. For those that do, use derivatives and algebra to find the exact values of all c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

$f (x) = 2^{x}, [a, b] = [0, 3]$

Sketch careful, labeled graphs of each function f in Exercises 63–82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of $f, f', a n d f'',$ and examine any relevant limits so that you can describe all key points and behaviors of f.

$f (x) = \frac{1}{x^{2} + 3}$

Sketch careful, labeled graphs of each function f in Exercises 63–82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of $f, f', a n d f'',$ and examine any relevant limits so that you can describe all key points and behaviors of f.

$f (x) = {(\ln x)}^{2} + 1$

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points.

$f (x) = 3^{x} - 2^{x}$

Find the critical points of each function f .Then use a graphing utility to determine whether f has a local minimum, a local maximum, or neither at each of these critical points .

$f (x) = \frac{I n 2 x}{x}$

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Calculus

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Short Answer

Find the possibility graph of its derivative f'.

Step by Step Solution

Step 1. Given

Step 2. Explanation

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Calculus

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Short Answer

Find the possibility graph of its derivative f'.

Step by Step Solution

Step 1. Given

Step 2. Explanation

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