(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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).

3. 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

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# Langrange Multipliers and Minimum Distance

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