Lagrange Multipliers: Lecture 13: Denis Auroux, MIT OCW To find an extremum for a function f of several variables subject to a constraint g = k, find where the level sets of f are tangent to the level sets of the constraint g. Since they share the same tangent space, the normal vectors will be parallel. Recall that the gradient vector is perpendicular to its tangent space and to its level sets. So candidates for an extremum will occur when the gradients of f and g are parallel, that is, when those vectors are proportional. The scalar of proportionality is called a Lagrange multiplier. He concludes with a wonderful example to minimize the total surface area of a tetrahedron given a triangular base and given volume. He minimizes a formula for surface area by looking at a point perpendicular to the three sides in the base of the given triangle https://youtube/watch?v=15HVevXRsBA
Posted on: Mon, 26 Aug 2013 19:27:06 +0000
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