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!