y=¾cos(2x-π/3), dy/dx=-(3/2)sin(2x-π/3)=0 at turning points.
Therefore, 2x-π/3=πn where n is an integer, 2x=πn+π/3, x=πn/2+π/6.
n=-1: x=-π/2+π/6=-⅓π, y=¾cos(-π)=¾cos(π)=-¾
n=0: x=⅙π, y=¾cos(0)=¾
n=1: x=π/2+π/6=⅔π, y=¾cos(π)=-¾
So we have three turning points: (-⅓π,-¾), (⅙π,¾), (⅔π,-¾).
Since y goes from - to + to - between these points, these are:
MIN(-⅓π,-¾), MAX(⅙π,¾), MIN(⅔π,-¾).