Mean value Theorem :

If  is continuous on  and differentiable on open interval , then there exists a number  in  such that .

The function  is continuous at the point  in its domain if :

1.  exists,

2. .

Now observe the graph :

Here  and .

.

So the graph has discontinuity at  since it has hole at .

The function is not continuous on the closed interval .

Therefore the mean value theorem does not apply to the function.

The mean value theorem does not apply to the function.