Lagrange Multipliers solve constrained optimization problems. That is, it is a technique for finding maximum or minimum values of a function subject to some constraint, like finding the highest point on a mountain subject to the fact you can only walk along a trail. In this video we study the contour lines or level curves of a function and see geometrically why they are maximized when they are tangent to the constraint curve. That tangency condition leads to the algebraic formula that the gradient of f is equal to lambda times the gradient of g. In this video we will visualize the geometric meaning and then walk through a concrete example.

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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