Alright so I have a few problems using the derivative tests and I understand like if f' changes from positive to negative at c, the f has a local maximum at c. But then for like this problem cos^2x - 2sinx, 0 < x < 2pie those are less then or equal to don't know how to show that. And take the derivative -2sinx-2cosx so we have a sign change but whats c? So here are a couple problems i need help on.

Find intervals at which f is increasing and decreasing, find local max and min values of f, and find the intervals of concavity and inflection points. for :

f(x) = cos^2x - 2 sinx, 0 < x < 2pie (less then or equal to)

Thanks for any help.