This paper analyses the situation in teaching mathematics at faculties of engineering in Bosnia and Herzegovina based on research conducted using a test comprising ten extremal problems administered to second-year students enrolled in the four most popular engineering study programs. The aim of the research was to review the local mathematics teacher training and refine the traditional methodology of teaching mathematics, as well as to analyse teaching the subject to students of engineering, especially their understanding and mastering topics such as differential calculus, more specifically the derivative of functions of one or more variables, and its application in solving extremal problems and developing students’ ability to apply the acquired knowledge in learning physics and specific engineering subjects. The obtained results were used to make recommendations as to how to improve the teaching of mathematics at local universities.