# Fermat's theorem (stationary points) of higher dimensions

• Mar 7th 2013, 01:03 AM
ianchenmu
Fermat's theorem (stationary points) of higher dimensions
Let $E\subset \mathbb{R}^n$ and $f:E\rightarrow\mathbb{R}$ be a continuous function. Prove that if $a$ is a local maximum point for $f$, then either $f$ is differentiable at $x=a$ with $Df(a)=0$ or $f$ is not differentiable at $a$.