Answer to Question #19641 in Real Analysis for shah

Question

Let I:=[a,b] and let f: I→R be differentiable at c ∈ I. Show that for every ϵ >0 there exists δ>0 such that if 0<|x-y|<δ and a ≤x ≤c ≤y ≤b, then |[((f(x)-f(y))/(x-y)] -f '(c)|<ϵ.