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Q. 25

Expert-verified

Calculus

Found in: Page 261

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. Calculation

From the above graph, f'>0 at (3, $\infty$ ); the function is increasing from (3,0); the graph f'<0 at (-0,1) and (1,3) where the function is decreasing.

Most popular questions for Math Textbooks

Use the second-derivative test to determine the local extrema of each function $f$ in Exercises $29 - 40$ . If the second-derivative test fails, you may use the first-derivative test. Then verify your algebraic answers with graphs from a calculator or graphing utility. (Note: These are the same functions that you examined with the first-derivative test in Exercises $39 - 50$ of Section $3.2$ .)

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

Last night at 6 p.m., Linda got up from her blue easy chair. She did not return to her easy chair until she sat down again at 8 p.m. Let s(t) be the distance between Linda and her easy chair t minutes after 6 p.m. last night.

(a) Sketch a possible graph of s(t), and describe what Linda did between 6 p.m. and 8 p.m. according to your graph. (Questions to think about: Will Linda necessarily move in a continuous and differentiable way? What are good ranges for t and s?

(b) Use Rolle’s Theorem to show that at some point between 6 p.m. and 8 p.m., Linda’s velocity v(t) with respect to the easy chair was zero. Find such a place on the graph of s(t).

Use the definition of the derivative to find f' for each function f.

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

Find the critical points of the function

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

Find the possibility graph of its derivative f'.

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