Multivariable critical points

[full sequoia]

From Wikipedia

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[full sequoia]

So my question is, what are "those cases not listed above"? Is it only when there exist an eigenvalue equal to 0? Or am I missing something? Like, I cannot think of any other case, but the way it is worded makes it seems like there are more

[cunning meteor]

yes

the only case not listed in the three main categories is when there exists at least one eigenvalue equal to 0 (with other eigenvalues being non-zero)

[full sequoia]

I see, thanks!

Is there anything I can do in that case? To determine what it is

[cunning meteor]

yes
Use higher-order derivatives, Examine the function directly, Perturb the Hessian choose one

well to clarify

when at least one eigenvalue is zero the second derivative test becomes inconclusive because the hessian matrix does not provide enough information to classify the critical point

in that case you can use on of the methods listed

[full sequoia]

I'll check those out. Thanks!

+close

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