# Whether the statement, if f is differentiable and f ( − 1 ) = f ( 1 ) then there is a number c such that | c | &lt; 1 and f ′ ( c ) = 0 is true or false.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 4, Problem 4RQ
To determine

## Whether 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 is true or false.

Expert Solution

The given statement is true.

### Explanation of Solution

Reason:

The function f is a continuous function as f is differentiable function.

Also it is given that, f(1)=f(1) .

So, the local maximum or a local minimum occurs between x = −1 and x = 1.

There must be a point c such that, at the point c the value of the derivative is zero.

That is there exist a point c such that, |c|<1 and f(c)=0 .

Therefore, the given statement is true.

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