The function is ,  and .

Mean value theorem :

Let  be a function that satisfies the following three hypotheses.

1.  is continuous on .

2.  is differentiable on .

Then there is a number  in  such that .

Let us consider the function is continuous on the interval .

 for all values of .

The function is differentiable on the interval .

Then .

From the mean value theorem :

From the mean value theorem, .

But .

Therefore no function exist where .

The function does not exist where .