Lagrange Multipliers

Related Topics:
More Lessons for Engineering Mathematics

Math Worksheets

A series of free Engineering Mathematics video lessons. How to solve problems through the method of Lagrange multipliers?

Lagrange multipliers:
Extreme values of a function subject to a constraint Discuss and solve an example where the points on an ellipse are sought that maximize and minimize the function f(x,y) := xy. The method of solution involves an application of Lagrange multipliers. Such an example is seen in 1st and 2nd year university mathematics.
Lagrange multiplier example:
Minimizing a function subject to a constraint I discuss and solve a simple problem through the method of Lagrange multipliers. A function is required to be minimized subject to a constraint equation. Such an example is seen in 2nd-year university mathematics.

Multivariable Calculus: Directional derivative of $f(x,y)$
I present an example where I calculate the derivative of a function of two variables in a particular direction. In particular, I take the derivative of $f(x,y) := 1 - x^2/2 - y^4/4$ in the direction of the vector ${\bf u} := (1,1)$. I solve the problem and also talk about the geometric meaning of the directional derivative.
Lagrange multipliers example
This video shows how to apply the method of Lagrange multipliers to a max/min problem. Such ideas are seen in university mathematics.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.