已知函数y=cos^2x-sinx+3,x属于【π/6,2π/3】求函数最大值
问题描述：
已知函数y=cos^2x-sinx+3,x属于【π/6,2π/3】求函数最大值
答
(cosx)^2-sinx+3=1-(sinx)^2-sinx+3=-(sinx)^2-sinx+4=-(sinx)^2-sinx-1/4+1/4+4=-[(sinx)^2+sinx+1/4]+17/4=-(sinx+1/2)^2+17/4x∈【π/6,2π/3】当x=π/6时,函数y=cos^2x-sinx+3值最大=-(sinπ/6+1/2)^2+17/4=-(1/...