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Abstract: The construction of optimized models of real phenomena and processes is one of the main tasks of the applied mathematicians, and in general of any professional in any field of human activity. It is hardly possible to overestimate the importance of finding a way to maximize returns (profits, output of finished products, etc.) with minimal expenditure of almost always limited resources (financial, human, time, etc.). It is equally important that the school teacher and university lecturer of mathematics know how to instill taste and to form stable skills in solving optimization problems of their students. It is important to develop the skills of problem solving in secondary school where students often lose an interest in studying, especially mathematics. Meanwhile, to the conscious solution of the problems «on the maximum / minimum» the students with their teachers come only in the graduate classes, after studying the topic «Derivative» and in connection with the preparation for the compulsory Unified State Exam in mathematics containing such tasks. There is a sharp contradiction, as the basic skills of solving optimization problems should be formed in secondary school, but in fact they are formed in high school only. This requires the search for effective ways of teaching students to solve optimization problems without the reference to the topic of derivative. The possibility of applying extremal properties of a quadratic function for solving extremal (optimization) problems without unreasonable use of the derivative is considered. It is found that the extremal properties of a quadratic function not only allow efficiently solve rather complicated optimization problems, but also increase the motivation level of students to learning mathematics, including those who are of humanitarian and aesthetic orientation. Pedagogical investigation with the participation of students — future teachers of mathematics, revealed the need for targeted formation of sustainable skills in solving «non-differential» optimization problems in Bachelor students.