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## Lecture 13: Lagrange multipliers

Lecture 13: Lagrange multipliers

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Part of video series Calculus 3 Course acquired through MIT OpenCourseWare

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.

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Learn about Lagrange multipliers, what they are, and how to use them.

- Problem Set - A problem set with some problems from this lecture.
- Lecture Notes - Lecture Notes from this lesson.
- Transcript of Lesson - Written transcript from this lesson.
- Lagrange Multipliers Activity - A Java computer simulation applet for Lagrange multipliers.

- How do you find the minimum and maximum values of a function of several variables when the variables are not independent?
- What is a Lagrange multiplier and how do you find them?
- How do you find the point closest to the origin on the hyperbola xy = 3?
- How do you find where two level curves are tangent to each other?
- How would you build a pyramid with a given triangular base and volume to minimize the total surface area?

This video explains Lagrange multipliers, one of the more famous topics in Calculus, which carry over to problems in higher courses, such as Linear Algebra and Differential Equations. You will learn ways of minimizing values of a function, when all variables are not independent. A couple of interesting problems are carried to completion through almost the entire lecture.