Keyword: «largest and smallest value»

The article discusses the problem of learning how to solve problems for finding the largest and smallest values of a function in a basic school algebra course. The analysis of the Federal State Educational Standard, the Federal Work Program in Mathematics for Secondary schools, and recommended school textbooks was carried out. The analysis revealed that insufficient attention is paid to extreme tasks in the secondary school, and there is actually no systematic approach to solving them without using a derivative. The authors propose a methodological approach based on the identification of a key problem using the example of the Cauchy inequality for two non-negative numbers. The publication provides a formulation of the key task, examples of its use to find extremes, and specific recommendations for teachers. The proposed approach will make it possible to compensate for the lack of relevant materials in the educational literature and organize differentiated training.