The Student Room Group
Reply 1
Have you come across the Hessian matrix before?
Reply 2
Nope :-s
Reply 3
The Hessian is the matrix of mixed partial derivatives:

H=(2fx22fxy2fxy2fy2) H = \begin{pmatrix} \frac{\partial^2 f}{\partial x^2} & \frac{\partial^2 f}{\partial x \partial y}\\ \frac{\partial^2 f}{\partial x \partial y} & \frac{\partial^2 f}{\partial y^2} \end{pmatrix}.

If this matrix has +ve eigenvalues only, then the function is increasing in every direction, and hence we have a minimum. If we have only -ve eigenvalues, then we have a maximum. If the e.vs are mixed, then in some directions the function increases, and in others the function decreases, so we have a saddle point.
Reply 4
But my hessian matrix is just the zero matrix