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February 3, 2013 / like2think

A nice proof of implicit function theorem.

In order to make some clean up in my knowledge of mathematical programming, I’ve decided to reconsider Lagrange Multipliers Rule. As it always happens with calculus-related things, it required from me good understanding of prerequisites, and in this case it appeared, that it relies on Implicit Function Theorem.

In traditional courses of Calculus in soviet books it’s proved by induction on number of free variables. I strongly dislike such an approach, cause it doesn’t give any evidence why it’s valid. I’d like to share with you a wonderful explanation why it works:

Up: either the proof is a little bit wrong or I missed something in it: what is the domain of contracting function?



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