If f:[a, b] →R has a local minimum at p E (a, b) and f is differentiable at p, then prove that f'(p) = 0.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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then
prove
that f'(p) 0.
If f: la, b] → R has a local minimum at p E (a, b) and f is differentiable at p,
Transcribed Image Text:then prove that f'(p) 0. If f: la, b] → R has a local minimum at p E (a, b) and f is differentiable at p,
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