Hi, I would like to confirm that I have understood this correctly. The steps to find local maxima/minima of a function f(x1, ... , xn) are: 1) We find all the stationary points. 2) We form the Hessian matrix and calculate the determinants D1, D2.... Dn for a stationary point P we want to check. 3) We have the following cases: i) if Di > 0 for i = 1 to n then P is definately a local minimum point ii) if Di*(-1)^i > 0 for i = 1 to n then P is definately a local maximum point iii) if Dn = 0 this test cannot help us determine whether the point is a local minimum or maximum iv) in ALL other cases (for example Di = 0 for i other than n or Di with sign other than what i and ii indicate) we definately have a saddle point. Are iii and iv correct? More specifically, I would like a clarification on what exactly happens when we have one or more zero Di. Thanks in advance for your time.