MATH 2D Lecture Notes - Lecture 23: Lagrange Multiplier, Fast Fourier Transform, Carnitine Palmitoyltransferase IiExamPremium
Course CodeMATH 2D
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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
24742 4K2 for 21 12
121 8min 10,12 2
161 12 Max lo 2,12 Max
fl21 8min 1210,8
Andletglt guilt kconstant
ftilt guilt 77g Ttt
Andlet FLH fCrTt
F'ft If FIt Omustholdatcritical
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