高数二之求极值
问题描述:
高数二之求极值
求f(x,y)=x平方+xy+y平方+x-y+1的极值
答
df/dx=2x+y+1df/dy=2y+x-1令df/dx=0df/dy=0即2x+y+1=02y+x-1=0得x=-1y=1d²f(-1,1)/dx²=2d²f(-1,1)/dxdy = d²f(-1,1)/dydx = 1d²f(-1,1)/dy²=2det[2,1; 1,2]=2²-1²=3>0所以(...