Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

Q. 17

Expert-verified

Calculus

Found in: Page 260

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Determine the graph of a function f from the graph of its derivative f'.

The function f is shown in Graph II and its derivative f' is shown in Graph I.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given

The given two graphs are

Step 2. Explanation

The objective is to find one of the graph is shown as a function f and the other is its derivative

Now, to determine the graph of a function f from the graph of its derivative f'.

Observed form the second figure, the function f must be decreasing on the interval (-∞,-1)

and (0.8,2.6), and increasing on the interval (-1,0.8) and (2.6, $\infty$ ).

So, the one of the possible sketch of a function f that has these characteristics is shown in the graph II.

Therefore, the graph I indicates the derivative of a function f.

Hence, the function is shown in Graph II and its derivative f' is shown in Graph I

Most popular questions for Math Textbooks

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.

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

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.

$f (x) = \ln (x^{2} + 1), [a, b] = [0, 1]$

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.

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

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.

$f (x) = - x^{3} + 3 x^{2} - 7, [a, b] = [- 2, 3]$

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.

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

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free