Lagrange Multipliers
Objectives of the lab
The method of Lagrange multipliers is used to find the local extrema of a
function f(x) whose inputs are restricted to lie on an
implicitly-defined surface g(x)=k. As in, "Find the maximum
value of the function f(x,y)=x^2+y^2 when x and
y are constrained to lie on the ellipse
(x-1)^2+4*y^2=4."
The power of the method lies in the strictly mechanical nature of
the process: you compute something, plug in something, and chug out
the answer.
But we're an intellectually curious bunch, not content with such a
"black box" approach to mathematics. The purpose of this lab is to
expose the method of Lagrange multipliers for what it is -- a
geometric method based on gradient vector fields and their
relationship to level curves.
You will need to invoke Maple for this lab.
Outline
Next: The Geometry Behind Lagrange Multipliers
Robert E. Thurman<thurman@geom.umn.edu>
Document Created: Sat Jan 13 1996
Last modified: Mon Jan 15 14:17:11 1996