y=√3/2sin2x+(1+cos2x)/2
=√3/2sin2x+cos2x/2+1/2
=sin(2x+π/6)+1/2
所以最大值为3/2
最小值为-1/2
当2x+π/6=2kπ+π/2,即x=kπ+π/6,k属于Z,时取得最大值
当2x+π/6=2kπ-π/2.即x=kπ-π/3,k属于Z,时取得最小值