F(x, y) = x^2+y^2+x^2y+6 find the absolute max and min

has critical points where the partial derivatives simultaneously vanish:






So we have three critical points to consider, , , and .

The function has Hessian



At the critical points, we have




which means there is a minimum at (0, 0) of ;



which means is a saddle point; and



which means is also a saddle point.