Mathematics

Problem

Consider the function

g(x)=2\sin x-\sin 2x

on the interval

0\le x\le 2\pi

. At which of the following points does

g

attain its greatest local maximum within this interval? a)

x=\dfrac{\pi}{2}

x=\dfrac{4\pi}{3}

x=\dfrac{2\pi}{3}

x=\dfrac{5\pi}{6}