Topic: Critical Points and Local Extrema

Classifying Coupled Polynomial Critical Points

Symmetry and Structured Hessians at Critical Points

Common Errors in Critical-Point Classification

Higher-Order Analysis of Degenerate Three-Variable Points

Separable Functions and Coordinatewise Classification

Indefinite Hessians and Three-Variable Saddle Points

Semidefinite Hessians and Degenerate Three-Variable Points

Using Principal Minors in Three-Variable Tests

Sylvester’s Criterion for Definite Hessians

Classifying Three-Variable Hessians by Eigenvalues