I saw a few questions about classifying Lagrange Multiplier Theorem points, but none of them seem to address the Hessian specifically.
Say I use Lagrange Multiplier Theorem to minimize/maximize some function under some compact constraints and I get only one point. Assume that I can't assign some easy case to the function and compare it's values, and that I know the Hessian of the function in that point.
Can I classify the point as a maximum/minimum based on the eigenvalues of the Hessian?