Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 4 - Section 4.3 - How Derivatives Affect the Shape of a Graph - 4.3 Exercises - Page 306: 36

Answer

We can see a sketch of one possible graph below.

Work Step by Step

$x=0$ is a vertical asymptote. $f'(x) \gt 0$ if $x \lt -2$ The graph is increasing on the interval $(-\infty, -2)$ $f'(x) \lt 0$ if $x \gt -2, x \neq 0$ The graph is decreasing on the interval $(-2,0)\cup (0, \infty)$ $f''(x) \lt 0$ if $x \lt 0$ The graph is concave down on the interval $(-\infty, 0)$ $f''(x) \gt 0$ if $x \gt 0$ The graph is concave up on the interval $(0,\infty)$
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