PROPOSITION Let I be an open interval and suppose f : I → R is differentiable at c e I. If f has a local max or min at c, then f'(c) = 0.

College Algebra
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ISBN:9781938168383
Author:Jay Abramson
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Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Can you please prove the local min result for the proposition attached? Thank you. 

PROPOSITION
Let I be an open interval and suppose f : I → R is differentiable at c E I. If f
has a local max or min at c, then f'(c) = 0.
Transcribed Image Text:PROPOSITION Let I be an open interval and suppose f : I → R is differentiable at c E I. If f has a local max or min at c, then f'(c) = 0.
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