Calculus: Early Transcendentals 8th Edition

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

Chapter 4 - Review - True-False Quiz - Page 358: 6



Work Step by Step

Consider an example $f(x)=(x-2)^{4}$ and $f''(x)=12(x-2)^{2}$ Here $f''(2)=0$, but $f''(x)$ does not change sign, hence there is no inflection point. For there to be an inflection point, $f''(x)$ when $x\lt 2$ and $f''(x)$ when $x\gt 2$ must have opposite signs. Hence, the given statement is false.
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