求函数y=sin2x+√3*cos2x的最大值,最小值及周期,并求使函数取得最大值最小值的x的集合.

y=2(sin2xcosπ/3+cos2xsinπ/3)
=2sin(2x+π/3)
所以
最大值=2,最小值=-2
周期=2π/2=π
最大值时,2x+π/3=2kπ+π/2
2x=2kπ+π/6
x=kπ+π/12
即集合为{x|x=kπ+π/12,k∈Z}
最小值时,2x+π/3=2kπ+3π/2
2x=2kπ+7π/6
x=kπ+7π/12
即集合为{x|x=kπ+7π/12,k∈Z}