The implicit and inverse function theorems: easy proofs (Q2510991)

From the introduction: ``The objective of this paper is to present very simple and easy proofs of the implicit and inverse function theorems on a finite-dimensional Euclidean space. The lack of sophisticated tools used in its proof could make the implicit function theorem more accessible to an undergraduate audience. Besides following Dini's inductive approach, these demonstrations do not employ compactness arguments, the contraction principle or any fixed-point theorem. Instead of such tools, these proofs rely on the intermediate-value theorem and the mean-value theorem on the real line.''