Let's find all local maxima and minima by setting f'(x) = 0:

So: and that is all since has no real roots. So we know there is only one value such that

Now for the proof. Assume that there are 3 real roots so .

Now see if you can use Rolle's Theorem to finish off the proof, keeping in mind f(x) has only 1 value of x such that f'(x) = 0.