Step 1:

The function is .

Mean value theorem :

Let be a function that satisfies the following hypotheses :

1. is continuous on .

2. is differentiable on .

Then there is a number in such that,

.

Step 2:

The function is .

The function is  continuous on the interval .

Differentiate with respect to .

.

The function is differentiable on the interval .

The mean value theorem satisfies the hypothesis.

Then

Step 3:

From the mean value theorem :

.

Substitute in .

Substitute in .

Solution :

The function satisfies the mean value theorem on the interval .

.

and .