The function is  and .

Corollary :

If  for all values of  in the interval , then  is a constant on , then , where  is a constant.

The function is .

Differentiate  on each side with respect to .

.

If  then function is .

Differentiate  on each side with respect to .

.

Therefore .

Apply  theorem.

Here  is not a constant over the domain.

If  then function is .

Differentiate  on each side with respect to .

.

Therefore .

Apply theorem.

Then  is a constant over the domain.

But over all  is not a constant over the domain.

 is not a constant over the domain.