Assume that is differentiable. Let c be a critical point such that (c) > 0 [the

Assume that ƒ is differentiable.

Let c be a critical point such that ƒ"(c) > 0 [the case ƒ"(c)

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(a) Show that f" (c) = lim f'(c + h) h (b) Use (a) to show that there exists an open interval (a, b) containing c such that f'(x) < 0 if a < x < c and f'(x) > 0 if c < x < b. Conclude that f(c) is a local minimum.