Answered: 67. Proof of the Second Derivative Test… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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67. Proof of the Second Derivative Test Let c be a critical point such that f"(c) > 0 [the case f"(c) < 0 is similar].
(a) Show that f"(c) = lim
(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.
f'(c +h)

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