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Unread 25-11-2006, 23:52
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Astronouth7303 Astronouth7303 is offline
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Lagrange Multipliers

Ok, I'm having a problem understanding a question about Lagrange Multipliers.

Given the function f(x, y) = 16 − x2y2 and the constraint (x − 1)2 + (y − 1)2 = 4, find the maximum and minimum.

I've reduced it to the system:
  1. -2x = λ∙2x
  2. -2y = λ∙2y
  3. (x − 1)2 + (y − 1)2 = 4

There are a few ways to solve this:
  • Assume λ = -1, which gets you nowhere
  • Assume x = 0, for which y = 1 ± √3
  • Assume y = 0, for which x = 1 ± √3

I know that the real answer is when x = y, but I can't get that going forwards.

Anyone have suggestions as to how to approach it?
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