求函数f(x)=cos2x-sinx x属于[-π/4,π/4]的最大值

问题描述:

求函数f(x)=cos2x-sinx x属于[-π/4,π/4]的最大值

f(x)=cos2x-sinx
=1-2sin^2x-sinx
=1-2(sin^2x+1/2sinx+1/16)+1/8
=9/8-2(sinx+1/4)^2
当sinx+1/4=0时,sinx=-1/4>-1/2,则-π/6