y'=2cos2x-1
令y'=0,cos2x=1/2,x=±π/6
x=-π/2时,y=π/2
x=-π/6时,y=-√3/2+π/6
x=π/6时,y=√3/2-π/6
x=π/2时,y=-π/2
∴x=-π/2时y取最大值π/2
x=π/2时y取最小值-π/2