Optimization Problems in Spanish Differential Calculus Books Published in the 18th Century

Abstract

History of mathematics and mathematics education research allows us to know, among other issues: the influence that certain textbooks have had on the teaching of school mathematics, in academic or professional training, during a certain historical period; as well as the scientific advances achieved in each historical period and their incorporation into the teaching of the subject matter. In this work, we focus our attention on the applications of the method of finding maxima and minima included in the textbooks published during the 18th century in Spain. Specifically, we identify the approach of the algorithm used, the shortcomings or deficiencies that the posing of the proposed problems may have, the verification of the nature of the optimal points obtained and the consideration—or not—of the negative solutions in the process of resolution.