∂f/∂x=3x^2+6x-9=0 x²+2x-3=(x-1)(x+3)=0 x1=1,x2=-3
∂f/∂y=-3y²+6y=0 y²-2y=y(y-2) y1=0 y2=2
A=∂²f/∂x²=6x+6
C=∂²f/∂y²=-6y+6
B=∂²f/∂x∂y=0
△=AC-B²
得到f(x,y)的四個穩(wěn)定點(diǎn):P1(1,0),P2(1,2),P3(-3,0),P4(-3,2)
(1)對P1點(diǎn):A=12>0,B=0,C=6>0 △=AC-B²=72>0 f(1,0)=-5 為極小值;
(2)對P2,P3點(diǎn)不是極值點(diǎn);
(3)對P4點(diǎn):A=-12