Question:

Let f:[a,b]-> R be a continuous function on the closed interval [a,b] and differentiable on the open interval (a,b). Show that for any c in (a,b) that is not a point of maximum of minimum for f', there exist in (a,b) such that:

This seems so matter-of-fact to me, and I know it's simply a sort of inversion of the Mean value Theorem, but I can't see how I would approach this. It looked really easy at first sight, but I'm lost..

All I know is that if there's an interval (x1,x2), there is at least one point such that the derivative at that point is equal to . (Mean Value Theorem). But I feel like it's not applicable in this proof..

Suggestions please? Thank you!