Hi, I need help proving this:

Let U be an open set in R^n, f:U--->R be of class C^2 and Gradient of f(a) = 0, a is an element of S contained in U where S is compact and convex.

Prove that there exists a constant M such that:

|f(x)-f(a)| <= M* |x-a|^2 for all x in S.

Thanks a lot.