- #1
schaefera
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Homework Statement
Use the method of Lagrange multipliers to find the points on the ellipse (x^2)+(2y^2)=2 that are closest to and farthest from the line x-y=2.
Homework Equations
I know that to do the lagrange I have to take the gradient of a function f and set it equal to some unknown constant times the gradient of my constraint (function g).
The Attempt at a Solution
I believe my constraint, g(x,y) should be the ellipse itself, so g(x,y)=(x^2)+(2y^2)-2 and [gradient of g]= {2x, 4y}.
What I don't know, however, is what is the function f I use? I think it has something to do with the distance formula, but I can't quite get my finger on what. Any help is greatly appreciated-- I feel like I'm very close to finding the answer, but am just missing one important step.
Thanks!
Austin