Chapter 5, Problem 5.10TE

Let $f\left(x\right)$ denote the probability density function of a normal random variable with mean $\mu$, and variance ${\sigma }^2$. Show that $\mu -\sigma$ and $\mu +\sigma$ are points of inflection of this function. That is, show that $f\text{'}\text{'}\left(x\right)=0$ when $x=\mu -\sigma$ or $x=\mu +\sigma$.