I have a test in 2 days and I can't figure out why I need the hessian to be positive definite to distinguish extrema. In other words, why do we need the condition $$w^{T} \cdot \nabla_{x}^{2}L(a,\lambda) \cdot w > 0$$
2026-03-30 03:03:27.1774839807
Why the hessian needs to be positive definite to distinguish extrema?
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Hint: Write the Taylor expansion up to second derivative .