The function is , .

Rolles Theorem :

Let be a function that satisfies the following three hypotheses.

1. is continuous on .

2. is differentiable on .

3. .

Then there is a number  in such that .

The function is .

The function  is continuous on the interval , because it is a polynomial.

Differentiate on each side with respect to .

 is differentiable on the open interval , which satisfies the Rolles Theorem.

Check  at the end points :

Substitute in .

Substitute in .

 , hence Rolls theorem is applicable on .

Find the value of , such that .

From then .

If , then .

is not in the interval .

Hence it is not considered.

If , then .

Therefore .

.