convex, twice differentiable functions Show that if $f:(a,b) \to \mathbb{R}$ is convex, twice differentiable on $(a,b)$ and $c$ is a stationary point, then $c$ is a local minimum point.
I have gone round in circles with this question and am now completely lost and would appreciate any help given

Quick answer: a convex (differentiable) function always lies above its tangent lines. The tangent line at $c$ is $y=f(c)$ because $Df(c)=0$. Therefore $f(x) \geq f(c)$ for every $x$.
