How do you find all local maximum and minimum points using the second derivative test given #y=cos^2x-sin^2x#?
we do not really need derivatives because we know that
However we can check:
so the critical points occur for:
and in fact:
#y''(2kpi) = -4 < 0#so these points are maximums, and
#y''((2k+1pi)) = 4 > 0#so these points are minimums.