find critical points 2costheta + sin^2theta

We are asked to find the critical points for y=2cos theta + sin^2 theta :
Critical points of a function are where the first derivative of the function is zero or fails to exist. So we need to find y' and set it equal to zero.
y'=-2sin theta + 2sin theta cos theta , the second term using the power rule and the chain rule. This function exists everywhere, so we need only find the zeros:
-2sin theta + 2 sin theta cos theta=0
2sin theta (-1+cos theta)=0
Then either sin theta = 0 " or " -1+cos theta = 0
sin theta =0 ==> 0=k pi, k in ZZ and cos theta = 1 ==> theta = 2k pi, k in ZZ
Thus the critical points are all whole number multiples of pi.
(Note that the critical points are the only points where relative extrema can exist: from the graph we see that at each multiple of pi there is a maximum or minimum.)
The graph:
http://mathworld.wolfram.com/CriticalPoint.html