find extrema of f(x) = x + 2cosx on the interval [-pi, pi]

I got x = pi/6, and x=5pi/6. One is a min, and one is a max, but the book also got x= -2.

Can someone explain how they got this?

Question

find extrema of f(x) = x + 2cosx on the interval [-pi, pi] 

I got x = pi/6, and x=5pi/6. One is a min, and one is a max, but the book also got x= -2.

Can someone explain how they got this?

anonymous · Answer

lets check it$$f'(x)=1-2\sin x=0$$gives$$\sin x=\frac{1}{2}$$x=-2 cant be one of extremas

anonymous · Answer

ithink what u got is right :)

anonymous · Answer

@mukushla This is a screenshot of the answer from the textbook. I'm not sure where the two came from, but it is somehow a part of the answer -_-;; Thanks for replying though XD

anonymous · Answer

yw :)