Topic: Critical Points and Local Extrema

Three-Variable Hessians and Curvature

The Three-Variable Second Derivative Test

Classifying Polynomial Surfaces in Two Variables

Critical-Point Systems in Three Variables

Higher-Order Terms at Degenerate Two-Variable Points

Recognizing Saddle Points from Indefinite Hessians

When the Two-Variable Test Is Inconclusive

The Two-Variable Hessian Determinant Test

Why the Two-Variable Determinant Test Works

Taylor Expansion Behind the Second Derivative Test