This book outlines some elementary (i.e., not requiring knowledge of differential calculus) ways to solve problems at maximum and minimum. The book is designed for high school students who want to get at least a general idea of ​ ​ the nature of the problems considered in higher mathematics. The presented material can be used in the work of the school mathematical circle. However, I think that it will be useful for a student of a technical university, pedagogical institute or university, even "dedicated" to the secrets of mathematical analysis, to read such a book.