Zur Rechtfertigung mathematischer Unterrichtsinhalte: Das Beispiel „Mittelwertsatz der Differentialrechnung“

Abstract

It is shown that the historical role of the mean value lemma on derivatives is usually overestimated. In particular, the values of c where f’(c) equals the slope of the chord have been considered inessential until recently. Moreover, the lemma can be replaced by equivalent ones in the calculus curriculum. Some reasons both against and for including it in calculus teaching are discussed, as well as a proposal how to teach the lemma if necessary.