发布时间：2019-08-08 14:32:19
Y=sin²(2x-π/6)-sin(2x-π/6)
=[sin(2x-π/6)-1/2]²-1/4
∵0≤x≤π/2
∴-π/6≤2x-π/6≤5π/6
∴-1/2≤sin(2x-π/6)≤1
∴-1≤sin(2x-π/6)-1/2≤1/2
0≤[sin(2x-π/6)-1/2]²≤1
-1/4≤[sin(2x-π/6)-1/2]²-1/4≤3/4
值域为：[-1/4，3/4]
因为Y‘=2[2sin（2x-π/6）cos（2x-π/6）－cos（2x-π/6）]
=2cos（2x-π/6）[2sin（2x-π/6）－1 ]
则驻点：2x－π/6+kπ=π/2+kπ，x=（π/6+π/2）÷2=π/6
因为x=π/6，该点的左导数＜0，右侧导数＞0，所以x=π/6是最小值
值域为≥0