求f(x,y)=4(x-y)-x^2-y^2的极值
问题描述：
求f(x,y)=4(x-y)-x^2-y^2的极值
答
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