## Calculus: Early Transcendentals 8th Edition

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.