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Assume that is differentiable on a ≤ x ≤ b and that f (b) < f (a). Show that f' is negative at some point between a and b.

Assume that is differentiable on a ≤ x ≤ b and that f (b) < f (a). Show that f' is negative at some point between a and b.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Assume that is differentiable on a ≤ x ≤ b and that ƒ (b) < f (a). Show that f' is negative at some point between a and b.
Transcribed Image Text:Assume that is differentiable on a ≤ x ≤ b and that ƒ (b) < f (a). Show that f' is negative at some point between a and b.
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