Theorem : Let f be defined on [a, b] , if f has a local minimum at a point x € (a, b), and if f'(x) exists , then f'(x) = 0.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
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please prove this theorem?

Theorem :
Let f be defined on [a, b] , if f has a local minimum at a
point x E (a, b), and if f'(x) exists , then f'(x) = 0.
Transcribed Image Text:Theorem : Let f be defined on [a, b] , if f has a local minimum at a point x E (a, b), and if f'(x) exists , then f'(x) = 0.
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