"Show that, at a local max or min of $\displaystyle ||\vec{r}(t)||$, the vector $\displaystyle r'(t)$ is perpendicular to $\displaystyle \vec{r}(t)$"

I think that if $\displaystyle f(t) = ||\vec{r}(t)||^2$, then the local min/max of $\displaystyle f(x)$ should be the same as $\displaystyle ||\vec{r}(t)||$, but I am not quite sure how to proceed with the rest of the question after that or how to show that $\displaystyle r'(t)$ is perpendicular to $\displaystyle \vec{r}(t)$.