The function is , at the point .

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 , at the point .

Substitute .

Substitute .

.

But function is not continuous at .

When , .

Hence function is not continuous on .

; but  f is not continuous on .