Cultivating optimization intuition in engineering education through multimethodological problem solving

This paper presents a m.ulti-methodological approach to solving optimization problems within the framework of engineering education. While traditional calculusbased methods focusing on derivatives are the standard pedagogical tool, they often fail to provide students with a deep physical and geometric intuition. We analyze several complex optimization cases, including radical sums, structural trapezoidal geometry, and fundamental mathematical constants, to demonstrate how visualgeometric methods can yield more efficient and insightful solutions. The results suggest that integrating these "short-cut" geometric strategies alongside traditional
calculus enhances the analytical capabilities of engineering students and fosters a more robust understanding of mathematical modeling in practical applications.