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/contour-lines 2. https://mathoverflow.net/questions/1977/why-is-the-gradient-normal Further Reading: 1. The Variational Principles of Mechanics, Cornelius Lanczos, 2.1-2.6 2. http://www.math.toronto.edu/courses/mat237y1/20189/notes/Chapter2/S2.8.html 3. http://abel.math.harvard.edu/~knill/teaching/summer2014/exhibits/lagrange/genesis_lagrangemultpliers.pdf 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