求下列函数的最大值,最小值及单调范围:1.y=3sin(2x+3分之π)+3

唉。。。

1）正弦型函数
因-1≤sin(2x+π/3)≤1,则0≤3sin(2x+π/3)+3≤6
所以ymax=6,ymin=0
单调增区间：-π/2+2kπ≤2x+π/3≤π/2+2kπ,即-5π/12+kπ≤x≤π/12+kπ
单调减区间：π/2+2kπ≤2x+π/3≤3π/2+2kπ,即π/12+kπ≤x≤7π/12+kπ

2）正弦型函数
因-1≤sin(-3x+π/6)≤1,则-4≤2sin(-3x+π/6)-2≤0
所以ymax=0,ymin=-4
单调增区间：-π/2+2kπ≤-3x+π/6≤π/2+2kπ,即-π/9+2kπ/3≤x≤2π/9+2kπ/3
单调减区间：π/2+2kπ≤-3x+π/6≤3π/2+2kπ,即-4π/9+2kπ/3≤x≤-π/9+2kπ/3

3）余弦型函数
因-1≤cos(2x-π/6)≤1,则-1≤-3cos(2x-π/6)+1≤3
所以ymax=3,ymin=-1
单调增区间：2kπ≤2x-π/6≤π+2kπ,即π/12+kπ≤x≤5π/12+kπ
单调减区间：-π+2kπ≤2x-π/6≤2kπ,即-5π/12+kπ≤x≤π/12+kπ