Step 1:

The function is  .

Mean value theorem :

Let f be a function that satisfies the following three hypotheses :

1. f is continuous on 

2. f is differentiable on 

Then there is a number c in  such that  .

Step 2:

Let x > 0 , .

Let us consider a number c in .

Since the hypotheses of the Mean Value Theorem are satisfied,

we get  .

Differentiate  with respect to .

Substitute in the mean value theorem.

If x > 0, then c > 0 and, therefore, .

So .

Solution: