Question

求f(x,y)=4(x-y)-x^2-y^2的极值

Answer 1

f(x,y)=4(x-y)-x^2-y^2=-(x-2)²-(y+2)²+8

因为(x-2)²≥0,(y-2)²≥0

所以f(x,y)=4(x-y)-x^2-y^2=-(x-2)²-(y+2)²+8≤8

所以f(x,y)=4(x-y)-x^2-y^2存在最大值8,且此时x=2,y=-2