## Archive for August 2010

### Functions with exactly one stationary point

August 9, 2010

Let $f:\mathbb{R}^n\rightarrow \mathbb{R}$ be a continuous differentiable function, with exactly one stationary point $x$, and suppose that this point is a local minimum. If $n=1$ it is easy to see that $x$ must be a global minimum, but what if $n\geq 2$?