Lecture 17, 9/30/2022. This page is for Section 1 only.
ACMS 20550: Applied Mathematics Method I
Instructor: Bei Hu, b1hu@nd.edu, Hurley 174A
Constraint; Lagrange Multipliers
We have leart (a) elimination method; (b) implicit differentiation method;
Lagrange Multiplier method:
Finding the max/min of $ f(x,y) $ under the constraint $\phi(x,y)=$const. is the same as finding max/min of
$F(x,y) = f(x,y)+\lambda \phi(x,y)$ with $\phi(x,y)=$const.
Endpoint (Boundary poibnt). To find max/min, compare values at all points listed below:
(a) points where 1st derivatives are zero (horizantal tangent);
(b) end points;
(c) corner point(s);