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, 2.12.6
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