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Classifying critical points in 3D, the indeterminant case

When finding the critical points of a function, z=f(x,y), and a critical point has a hessian matrix with the determinant equal to zero, how do you classify the critical point?

Please help!

Thanks in advance! :biggrin:

Reply 1

BlueSam3

Use higher order tests, exactly as you would in the one-dimensional case.

Reply 2

supperrabbit

Original post by BlueSam3

Use higher order tests, exactly as you would in the one-dimensional case.

Could you please be more specific? What tests should i use exactly?

Also, i think you mean the two dimension case...

Reply 3

BlueSam3

Original post by supperrabbit

Could you please be more specific? What tests should i use exactly?

Also, i think you mean the two dimension case...

No, I mean the one dimensional case, of functions

\mathbb{R}\to\mathbb{R}

.

And the tests are basically exactly what you'd expect from generalising the versions for the one dimensional case.

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