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**limddavid** 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 $\displaystyle x_1,x_2$ in (a,b) such that:

$\displaystyle f'(c)=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

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..