# Lagrange Multipliers

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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.

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