Suppose f'(x) < 0 < f"(x), for x < a, and f'(x) > 0 > f"(x), for x > a. Prove that f is not differentiable at a. Assume f is differentiable at a and apply the Mean Value Theorem to f'.) More generally, show that if f' and f" change sign at the same point, then f is not differentiable at that point.