求函数f(x,y)=4(x-y)-x-y的极值

题目

求函数f(x,y)=4(x-y)-x-y的极值

答案

f(x,y)=4(x-y)-x^2-y^2,
=> fx=4-2x,fy=-4-2y;
=> fxx=-2,fxy=0,fyy=-2;
=>A=-2,B=0,C=-2,
=> AC-B^2>0,且A x=2,y=-2,
=> 极大值为 f(2,-2)=16-4-4=8.