   Chapter 3.R, Problem 4TFQ

Chapter
Section
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or given an example that disproves the statement.If f is differentiable and f ( − 1 ) = f ( 1 ) , then there is a number c such that | c | < 1 and f ' ( c ) = 0 .

To determine

Whether the given statement is true or false

Explanation

c<1  -1<c<1  c ϵ (-1 , 1 )

Since the function is differentiable, it must be continuous. So by Mean Value Theorem,

f'c= f1

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