Which direction makes a multivariable function increase fastest? Learn how the gradient packages partial derivatives, how to calculate directional derivatives with unit vectors and dot products, and why gradients cross level curves at right angles.
Why do gradients become parallel in constrained optimization? This Woody Calculus lesson explains the geometry and algebra of Lagrange multipliers, derives the system ∇f = λ∇g, and solves complete rectangle and box optimization examples.