Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - Review - True-False Quiz - Page 285: 1



Work Step by Step

When $f'(c)=0$ is only means that the tangent line to f at $x =c$ is horizontal. The function $f(x)=x^{3}$ has $f'(x)=2x^{2}$ $f'(0)=0$ but $f'(x)\gt 0$ and increasing for all other $x$. In this case $x=c$ is an inflection point and not a local maximum or minimum. Hence, the given statement is false.
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