Maximum/minimum problems solved using an algebraic way

This article describes some problems of the maximum/minimum type, which are generally solved using calculus at secondary school, but which here are solved algebraically. We prove six algebraic properties and then apply them to this kind of problem. This didactic approach allows pupils to solve these problems even at the beginning of secondary school, when teachers dedicate considerable time to geometry, rather than waiting until the study of mathematical analysis at the end of secondary school.