Second Derivatives and Convexity
Curvature, the Hessian, and Globally Well-Behaved Functions
Second derivatives capture curvature — how fast a function bends. The Hessian matrix organizes all second partials, powers the second derivative test, and unlocks the powerful theory of convex functions where local minima are guaranteed to be global.
Sections
Second Partial Derivatives
8 min · 4 quiz questions
Symmetry of Mixed Partials
6 min · 4 quiz questions
The Hessian Matrix
7 min · 4 quiz questions
Hessian of a Quadratic
7 min · 4 quiz questions
Quadratic Approximation
8 min · 3 quiz questions
The Second Derivative Test
9 min · 5 quiz questions · Interactive diagram
Convex Sets
7 min · 4 quiz questions · Interactive diagram
Convex Functions
8 min · 5 quiz questions
Hessians and Convexity
8 min · 5 quiz questions