I'm struggling to understand an example we were given. The problem description is:
Let $f$ be a convex function in $E^n$. Prove that the set of subgradients of $f$ in a given point form a ... convex set.
I have the solution, but don't really understand it. According to my intuition, the set of subgradients form a non-convex set of the points in areas marked $y$ in the following picture:
What am I missing here? Thanks.