The problem is:
Let g be of class $C^1$ on $\Delta$⊂$ℝ^n$ and K be a compact subset of Δ. Show that there is a number C such that |g(s)-g(t)|≤C|s-t| for every s,t∈K.
I have proved that it is true when K is convex, but I do not know how to proceed. Anyone could help me to solve this question?