Lecture 13: Lagrange multipliers

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Lesson Summary:

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.

Lesson Description:

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.

Additional Resources:
Questions answered by this video:
  • 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?
  • Staff Review

    • Currently 4.0/5 Stars.
    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.