Try writing it out:
What is f'(x)?
So the mean value theorem says:
It is just simple algebra now.
The geometric mean of two positive numbersa 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.