The bull-in-a-china-shop method is to multiply out the five factors and then differentiate the resulting 5th degree polynomial function. Not too difficult really, just a bit of drudgery.
The other way is to apply the Chain Rule and the Product Rule to find the first derivative of the function. Certainly the more elegant way to do it.
Either way, once you have the first derivative, set it equal to zero. There will be a stationary point at every zero of the first derivative function.
Once you have the first derivative, you will note that it is a rather ugly 4th degree polynomial. But if you look at a graph of the original function (use a graphing application or your graphing calculator, or simply realize that the 5th degree polynomial has a zero at 2 with a multiplicity of 4) you will see that there are only two stationary points, one at 2 and one between 0 and 1, just about 2/3.
If you take the ugly mess of a 4th degree polynomial function that you get for a first derivative, you will find that you will be successful performing synthetic division three successive times with a divisor of 2. That will leave you with a simple linear equation the solution of which is the remaining stationary point.
