Under a suitable non-degeneracy condition on its partial derivatives, an equation relating several variables can be locally solved for one variable as a differentiable function of the others. It is a basic tool of multivariable calculus and differential geometry.
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StatementThe implicit function theorem gives sufficient conditions under which an equation relating several variables can be solved for one of those variables as a function of the others near a given point. 1 Classification
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Source Implicit Function Theorem (Wikipedia)
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1. Implicit Function Theorem (Wikipedia)
Wikimedia FoundationLead section, opening sentence
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F(x,y)=0 can also be specified as the graph of a function f
Proved By: Augustin-Louis Cauchy, Lead
Augustin-Louis Cauchy (1789-1857) is credited with the first rigorous form of the implicit function theorem.
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