Solve this business calculus problem please.

The statement is true. Consider the function $f:\mathbb{R}\rightarrow \mathbb{R}$ definied by $f(x):= x^3$

This function is differentiable over $(-\infty ,\infty)$ and $f'(x)=3x^2$ equals $0$ if and only if $x=0$.

But $f''(x)=6x$, so that $f''(0)=0$. This means $x=0$ is neither a local minimum nor a local maximum.

Moreover, $f''(x)$ changes its sign at $x=0$. This makes $x=0$ an inflection point.