The Lagrange multipliers are also called Lagrangian multipliers (e.g., Arfken 1985, p. 945). They can be used to find the extrema of a given multivariate function subject to the derivative constraints .
Here, and are functions with continuous first partial derivatives on the end of the open set also containing the curve and at any point on the curve (where is the gradient of the curve).
Extreme values of a function are usually subject to a constraint. You will need to discuss and solve an example where the points on an ellipse are sought such that maximize and minimize the function f(x,y) = xy.
The method of solution also involves an application of Lagrange multipliers. Such examples are mostly seen in 1st and 2nd year of university students specializing in the subject of mathematics.
This calculator is all about minimizing a function subject to a specific constraint. It also discusses and solves a simple problem through the method of Lagrange multipliers. Thus, we can say that a function is required to be minimized subject to a constraint equation.