Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - 1.1 Real Numbers, Functions, and Graphs - Exercises - Page 10: 50


$f(x)$ is increasing on (-$\infty$,0) $\cup$ (0,$\infty$)

Work Step by Step

$f$($x$) =$x^{3}$ $f'(x)$=$3x^{2}$ $f'(x)=0$ when $x=0$ Therefore, $x=0$ is the critical point of $f(x)$ and the only point at which the function is not increasing. When $x<0$, $f'(x)>0$ When $x>0$, $f'(x)>0$ Therefore, when x $\ne$ 0, $f(x)$ is increasing.
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.