二元函数,极值条件为其偏导数同时为0
z=f(x,y)=sinx+cosx+cos(x-y)
dz/dx=cosx-sinx-sin(x-y)=0
dz/dy=-sin(x-y)*(-1)=sin(x-y)=0
可得 sin(x-y)=0, cosx-sinx=0
即 x-y=kπ,x=π/4+nπ
∴cos(x-y)=±1,sinx=cosx=±√2/2
二者均取负数时,函数取得最小值fmin=-√2-1
二者均取正数时,函数取得最大值fmin=√2+1