Assume that f has at least two continuous derivatives on an interval containing a with f'(a) =

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Assume that f has at least two continuous derivatives on an interval containing a with f'(a) = 0. Use Taylor’s Theorem to prove the following version of the Second Derivative Test.

a. If f"(x) > 0 on some interval containing a, then f has a local minimum at a.

b. If f"(x) < 0 on some interval containing a, then f has a local maximum at a.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

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Question Posted: Apr 13, 2019 09:04 AM

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Assume that f has at least two continuous derivatives on an interval containing a with f'(a) =

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Consider the remainder after the first term of the Taylor serie...View the full answer

Calculus Early Transcendentals

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