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Q. 33

Expert-verified

Found in: Page 166

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

The graph is:

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information

We are given the associated slope function f' for some unknown function f and we need to sketch a possible graph of f.

Step 2. Finding the graph

The function increases from $- 1.4 < x < 0$ and $x > 1.4$ and decreases from $x < - 1.4$ and $0 < x < 1.4$ .

Most popular questions for Math Textbooks

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

$f (x) = {(5 {(3 x^{4} - 1)}^{3} + 3 x - 1)}^{100}$

Suppose $u (x) = \sqrt{3 x^{2} + 1}$ and $f (u) = \frac{u^{2} + 3 u^{5}}{1 - u}$ . Use the chain rule to find role="math" localid="1648356625815" $\frac{d}{d x} (f (u (x)))$ without first finding the formula for $f (u (x))$ .

Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.

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

Use the definition of the derivative to find $f'$ for each function $f$ in Exercises 34-59

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

In Exercises 69–80, determine whether or not $f$ is continuous and/or differentiable at the given value of $x$ . If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.

$f (x) = \{\begin{cases} x^{2}, i f x \leq 1 \\ 2 x - 1, i f x > 1, \end{cases} x = 1$

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Calculus

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Short Answer

Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

Step by Step Solution

Step 1. Given Information

Step 2. Finding the graph

Most popular questions for Math Textbooks

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Calculus

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Short Answer

Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.

Step by Step Solution

Step 1. Given Information

Step 2. Finding the graph

Most popular questions for Math Textbooks

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