Hi, I would like to confirm that I have understood this correctly.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Q on Second partial derivative test for functions of n variables

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