函数y=sin(x-派/3)sinx的最大值是

问题描述:

函数y=sin(x-派/3)sinx的最大值是

y'(x)=0
π/6

求导数为零点,代入原方程即可

y=sin(x-π/3)sinx
=1/2[cos(x-π/3-x)-cos(x-π/3+x)]
=1/2[1/2-cos(2x-π/3)]
=1/4-1/2cos(2x-π/3)
≤1/4-1/2×(-1)=3/4