Math Help - Mean Value Theorem (Confused)

1. Mean Value Theorem (Confused)

The geometric mean of two positive numbers
a and b is the number sqrt(ab).
Show that the value c in the conclusion of the Mean Value Theorem for f(x)= 1/x on the interval of positive numbers [a,b]is c = sqrt(ab).

I understand other problems with M.V.T. but I don't know how to aproach this one.

2. Try writing it out:
What is f'(x)?
$f'(x)=\left(\frac{1}{x}\right)'=-\frac{1}{x^2}$

So the mean value theorem says:

$f(b)-f(a)=f'(c)(b-a)$

It is just simple algebra now.