In this lesson on Lagrange multipliers, we learn how to solve min/max problems when variables are not independent, but rather constrained by some equation. The method involves finding points where the level curves of the function to be minimized/maximized and the constraint function are tangent to each other. This is done by setting the gradients of the two functions equal to each other, along with the constraint equation, and solving for the variables. This method is applicable in many fields, including physics and mathematics.
Learn about Lagrange multipliers, what they are, and how to use them.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.