求多元函数极值f(x,y)=sinx+cosy+cos(x-y),0≤x,y≤π/2

Question

求多元函数极值
f(x,y)=sinx+cosy+cos(x-y),0≤x,y≤π/2

Answer 1

极值就是求导fx=cosx-sin(x-y)=0
fy=-siny+sin(x-y)=0
x+y=pi/2
f(x,y)=1+0+0=1极小值这是
f(x,y)