Using Determinants for Determining Extreme Values of a Function of One Variable, Two Variables and Three Variables

Finding the maximum and minimum values of a function is essential in high school math. However, Vietnamese high school students have only been taught how to find the extreme values of a function of 1 variable. Seeing the extreme values of a function of 2 and 3 variables is a difficult problem for students. Using the determinants, our aim in this paper is to show the necessary and sufficient conditions for a continuous and differentiable function (1 variable, two variables, and three variables) to reach its maximum over a specified domain. Furthermore, our method can be used to find the extremes of n-variable differentiable functions.