True or false: if $f: \mathbb R^n \rightarrow \mathbb R$ is a convex function, $y \in \mathbb R^n$ is such that $f(y)=\min_x f(x)$, and $z \in \mathbb R^n$ is such that $\nabla f(z)=0$, then $y=z$.
This was a question on my exam, and i answered it as 'True' while the correct answer was 'False'. I just don't see how $y \neq z$, because it is specifically mentioned that f is a convex function...
