Implicit Function Theorem Example
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Implicit Function Theorem Example
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Implicit Function Theorem Assume that S is an open subset of Rn k and that F S Rk is a function of class C1 Assume also that a b is a point in S such that F a b 0 and det DyF a b 0 i The Implicit Function Theorem is a basic tool for analyzing extrema of diferentiable functions Definition 1 An equation of the form f x p y 1 implicitly defines x as a function of p on a domain P if there is a function on P for which f p p y for all p P It is traditional to assume that y 0 but not essential
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