无极值
f(x,y)=x^2y^2-4x^2y-6xy^2+24xy
对x求偏导得 y(x-3)(y-4)
对y求偏导得 x(x-6)(y-2)
稳定点为{0,0} {0,4} {3,2} {6,4} {6,0}
又f对x求两次偏导,记为fxx=2y^2-8y fyy=2x^2-12x fxy=4xy-8x-12y+24
所以f对应的海赛矩阵的行列式为P=fxx*fyy-fxy^2=
-12x^2y^2+48x^2y+72xy^2-192xy-64x^2-144y^2+384x+576y-576
将上述解代入,均有 P