Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.3 - How Derivatives Affect the Shape of a Graph - 4.3 Exercises - Page 301: 29

Answer

We can see a sketch of one possible graph below.
1558361280

Work Step by Step

$f'(5) = 0$ The slope of the graph is zero at $x = 5$ There could be a local maximum or a local minimum at this point. $f'(x) \lt 0$ if $x \lt 5$ The graph is decreasing on this interval. $f'(x) \gt 0$ if $x \gt 5$ The graph is increasing on this interval. $f''(2) = 0$ and $f''(8) = 0$ $x=2$ and $x=8$ are points of inflection. $f''(x) \lt 0$ if $x \lt 2$ or $x \gt 8$ The graph is concave down on these intervals. $f''(x) \gt 0$ if $2 \lt x \lt 8$ The graph is concave up on this interval. $\lim\limits_{x \to \infty}f(x) = 3$ $\lim\limits_{x \to -\infty}f(x) = 3$ There is a horizontal asymptote at $y=3$
Small 1558361280
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.