Solving Problems with Parameters Using Derivative
Solving Problems with Parameters Using Derivative
Mamikonyan Haykanush,
Pepanyan Armine
Key words: function, tangent of function, maximum value, minimum value, functional method, analysis of function
Problems with parameters play an important role in the school mathematics course. Students often experience challenges when solving such problems, considering them difficult or not knowing the methods for solving them. There’s no universal way to solve these problems, actually. There are analytical, functional, and graphical methods, but it’s not always clear which method will be effective for a given task, and there is often a need to combine the aforementioned methods.
In this paper, the functional method for solving problems containing a parameter is studied. It is based on analyzing the function or functions involved in the given problem using the derivative. By analyzing functions, you can also plot their graphs and perform a graphical analysis, visualizing the problem.
Several examples using the aforementioned method are provided. The importance of including such tasks in the educational process is justified. The advantages of the functional method for solving problems with parameters are also presented. Solving such problems contributes to the development of analytical thinking and the ability to generalize the results obtained of high school students.
DOI: https://doi.org/10.58726/27382923-2025.2-130