Answered: Let f(x) = C[0, 1] and be…

Let f(x) = C[0, 1] and be differentiable in (0, 1). Suppose f(0) = 0. Prove: if f(x) is not constantly 0 in (0, 1), then there exists ( = (0,1), such that ƒ (§) · ƒ’(C) > 0.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

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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Question

Let f(x) = C[0, 1] and be differentiable in (0, 1). Suppose f(0) = 0. Prove: if f(x) is
not constantly 0 in (0, 1), then there exists ( = (0,1), such that ƒ (§) · ƒ’(C) > 0.

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