(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For the function f(x, y) = xye^[-(x^2 + y^2)] find all the critical points and classify them each as a relative maximum, a relative minimum, or a saddle point.

2. Relevant equations

Partial differentiation and Hessian determinants.

3. The attempt at a solution

I get how to compute the derivatives. I also get how to compute the Hessian determinants. Basically, I get all the algebraic details but what I would like to ask about (at least for now) is why does the Hessian determinant Δ_p = -1 imply that P(0, 0) is a saddle point?

Any input would be greatly appreciated!

Thanks in advance!

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# Homework Help: Why does the Hessian determinant Δ_p = -1 imply that P(0, 0) is a saddle point?

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