求f(x,y)=x^3-y^3+3x^2-9x的极值.
问题描述：
求f(x,y)=x^3-y^3+3x^2-9x的极值.
答
求f(x,y)=x³-y³+3x²-9x的极值令∂f/∂x=3x²+6x-9=3(x²+2x-3)=3(x+3)(x-1)=0,得x₁=-3,x₂=1；再令∂f/∂y=-3y²=0,得y=0；故得驻点M(-3,0)；N(1,0)；A=...