Lagrange Multipliers

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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
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)
Present an example to calculate the derivative of a function of two variables in a particular direction. Take the derivative of f(x,y) := 1 - x²/2 - y⁴/4 in the direction of the vector u := (1,1). Solve the problem and discuss 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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