Interactive MATLAB GUI for exploring extreme values in bivariate functions

This paper presents the development of a graphical user interface (GUI) in MatLab designed to assist in the identification and classification of extreme values and saddle points of functions of two variables. Aimed at supporting mathematics and Physics education for university students and instructors, the tool integrates symbolic differentiation and the second derivative test to provide an interactive learning experience. Through three representative examples, the GUI demonstrates its ability to detect multiple critical points and visually convey their nature, enhancing conceptual understanding. While the method is effective in most cases, it is limited when the discriminant D equals zero, rendering the second derivative test inconclusive. Furthermore, the current implementation supports only two-variable functions; adapting it to higher dimensions would require further development. Overall, the GUI serves as a valuable educational aid for teaching and learning multivariable calculus concepts.