Suppose f'(x) < 0 < f(x), for x < a, and f'(x) > 0 > f(x), for

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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.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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