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 , over the interval .

The function  is continuous on the interval .

Substitute in the function.

Substitute in the function.

.

Differentiate on each side .

Denominator of the derivative function should not be zero.

 So the derivative of the function is not differentiable at .

is in the interval .

Hence Rolles theorem second hypothesis is not satisfied.

; but   is not differentiable at .