Intuition and Examples for Lagrange Multipliers (Animated)

We discuss the idea behind Lagrange Multipliers, why they work, as well as why and when they are useful.

External Images Used:  
1. https://www.greenbelly.co/pages/conto...
2. https://mathoverflow.net/questions/19...

Further Reading:
1. The Variational Principles of Mechanics, Cornelius Lanczos, 2.1-2.6
2. http://www.math.toronto.edu/courses/m...
3. http://abel.math.harvard.edu/~knill/t...

Timestamps:
0:00 - Introduction
0:18 - Free Optimization in 1 Dimension
1:30 - Constrained Optimization
2:25 - Auxiliary Equations
3:05 - Solving with Substitution
4:25 - Where Substitutions break down
7:17 - Lagrange Multipliers
9:23 - Types of Extrema
12:04 - Lagrange Multiplier Example
13:42 - Final Notes