Applications of multivariable derivatives videos

What is a tangent plane

Computing a tangent plane

Local linearization

Controlling a plane in space

What do quadratic approximations look like

Quadratic approximation formula, part 1

Quadratic approximation formula, part 2

Quadratic approximation example

The Hessian matrix

Vector form of multivariable quadratic approximation

Expressing a quadratic form with a matrix

Multivariable maxima and minima

Saddle points

Second partial derivative test

Warm up to the second partial derivative test

Second partial derivative test example, part 2

Second partial derivative test intuition

Second partial derivative test example, part 1

Constrained optimization introduction

Lagrange multipliers, using tangency to solve constrained optimization

Finishing the intro lagrange multiplier example

Lagrange multiplier example, part 1

The Lagrangian

Lagrange multiplier example, part 2

Proof for the meaning of Lagrange multipliers

Meaning of the Lagrange multiplier