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Math Help - Lagrange Proof Problem

  1. #1
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    Lagrange Proof Problem

    Lagrange Proof Problem-question3.jpg

    I have no idea how to solve this question, any advice and help much appreciated!
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  2. #2
    Member
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    Sep 2010
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    For (1) there is actually nothing to prove in my opinion. If x* \in X \subset R^n maximizes f(x) s.t. h(x) = c then it is clear that (II) follows from (I)

    For (2) imagine a function that has its absolute maximum in the negative domain of R^n and decreases the closer it gets to zero and even decreases further for any positive number. Let this e.g. be for R^1: 100 - (10 + x)^2. If you maximize this function for x you will get x* = -10. However, if you can only choose from the positive numbers (you might want to use Kuhn Tucker to prove this formally) your x* = 0. However, this differs to the solution for (I) thus you proved that (2) is wrong by counter example.
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