# MATH 2D Lecture Notes - Lecture 23: Lagrange Multiplier, Fast Fourier Transform, Carnitine Palmitoyltransferase IiExamPremium

by OC2512313

Department

MathematicsCourse Code

MATH 2DProfessor

WILKINSON, JStudy Guide

FinalThis

**preview**shows half of the first page. to view the full**3 pages of the document.**Math 2D Lecture 3A

14.8: Lagrange Multipliers

When solving for the maximum or minimum over a closed domain D,wehadtocheckfor

critical points in the interior of Dand also separately had to check the boundary ∂D

For example, what is the maximum or minimum of f(x, y)=2x2+3y2when x2+y2=4?

Unfortunately, the boundary extrema cannot always be solved using substitution.

So how do we ﬁnd the max or min of f(x, y)whentheconstraintg(x, y)=Kmust hold?

The method of Lagrange multipliers says that we can set of points satsifying both

Of(a, b)=λOg(a, b)forsomeλ∈Rand g(a, b)=K

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121 8min 10,12 2

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letTITI

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