Fonction constante et dérivée nulle : un résultat si trivial…

Abstract : We study various proofs of the characterization of constant functions, more precisely of the theorem: a derivable function, defined on a real interval, is constant if, and only if, its derivative is null. Our aim is to study the relationships of these proofs with the mathematical curriculum of secondary schools and the beginning of undergraduate studies in France, from various points of views (epistemological, historical, and didactical). This study leads to the construction of the mathematical site of the studied theorem and can serve as a basis for training activities around the fundamental theorems of elementary analysis.
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https://hal.univ-antilles.fr/hal-01529547
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Antoine Delcroix, Christian Silvy. Fonction constante et dérivée nulle : un résultat si trivial… . Recherches et Ressources en Éducation et Formation, 2009, pp.77-89. ⟨hal-01529547⟩

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