Mathematics

Problem

For

0\le x\le 2\pi

, consider the function

p(x)=\sin x+\cos 2x.

(a) Determine

p'(x)

and locate all critical points that lie in the open interval

(0,2\pi)

. (b) Classify each critical point as a point of local maximum or local minimum and compute the corresponding value of

p

. (c) Arrange the local maxima and minima obtained in descending order of their function values.