You will find it easier for others to follow if you tell us in words what you are trying to do rather than just dump a load of manipulation on the page.

The global maximum (minimum) will be either a calculus type maximum (minimum) or it will occur at a boundary point. You have the derivative correct:

Now a calculus type critical point occurs where the derivative is zero so we look at the roots of:

which are , and , but we drop the as it is outside the interval of interest.

So now you need to examine the value of the function at , , and .

(By the way the question is asking for the maximum (minimum) of the function not the value of where it attains the maximum (minimum) )

CB