BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 4RQ

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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