The function is and the interval 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 .

Substitute in .

.

Substitute in .

.

.

The function is  and the interval is .

A function  is continuous when, for every value  in its domain,  is defined, and .

Consider the number  as .

.

Since the function  is undefined at , it is discontinuous on the interval .

Since the function is discontinuous on the interval , it does not satisfies the Rolles Theorem.

.

The function is discontinuous on the interval , it does not satisfies the Rolles Theorem.