Le théorème de Lagrange en mathématiques et en économie: une étude didactique du savoir enseigné

Because of its many uses, the constrained optimization problem is presented in most undergraduate mathematics courses dealing with calculus for both mathematicians and economists. Our research focuses on the teaching of Lagrange's Theorem in both branches of study, mathematics and economics. This paper addresses two objectives. First, we describe our epistemological reference model of the didactic transposition of Lagrange's Theorem in university courses. Secondly, we compare two mathematics courses dealing with Lagrange's Theorem given at the universities of Namur and Liège by means of this model and the Anthropological Theory of Didactics. This comparison is evidence of the manifold designs the teaching of Lagrange's Theorem can take.