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: 51


f is increasing on $(0,\infty)$

Work Step by Step

$f(x)=x^{4}$ $f'(x)=4x^{3}$ f'(x)=0 when x=0. Therefore, x=0 is the critical point of f. When x<0, f'(x)<0. For example, $f'(-2)=4\times(-2)^{3}=-32$. $\implies\, $ f is decreasing on $(-\infty,0)$. When x>0, f'(x)>0 $\implies\, $ f is increasing on $(0,\infty)$
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