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Final

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


Department
Mathematics
Course Code
MATH 2D
Professor
WILKINSON, J
Study Guide
Final

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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)forsomeλRand g(a, b)=K
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War
Mtg
24742 4K2 for 21 12
FIXy22314 21
12 X2f'tx2x
Ix OxO
f
121 8min 10,12 2
f
161 12 Max lo 2,12 Max
fl21 8min 1210,8
210,8 min
letTITI
be
the
spacecurvesatisfyingguilt
1k
Andletglt guilt kconstant
function
ftilt guilt 77g Ttt
Andlet FLH fCrTt
F'ft If FIt Omustholdatcritical
point
soagHTgmustholdforanyextremay
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