Determine local max., local min., and saddle points of the following function: $4x + 4y + x^2y + xy^2$
I know that we take the gradient vector and set it equal to zero to find the critical points. And observe the behavior of the determinant to decide whether a point is a saddle point,local max, or local min.
The gradient that I found was:$<4+2xy+y^2, 4+x^2+2xy>$. When I set them equal to zero, I'm unable to solve the system of equations.
Any help is appreciated.