Step-by-Step Function Analysis: ChatGPT’s Performance and Its Role in Supporting Student Understanding

Abstract

This study examines the potential of ChatGPT as a complementary tool for teaching function analysis, with a particular focus on economics students. While traditional computer algebra systems provide correct results, ChatGPT adds value through step-by-step explanations and intuitive analogies. The model was tasked with analyzing the function (f(x)=x^4-10x^2+9), producing both formal mathematical solutions and accessible explanations. Results show that the AI can accurately determine zeros, extrema, and inflection points while linking these outcomes to economic decision-making, such as cost minimization and profit maximization. This enables students to view function analysis not only as a technical procedure but also as a tool for real-world applications. However, the findings emphasize that AI should be regarded as a pedagogical enhancement rather than a replacement for the teacher, whose role remains essential in providing guidance, motivation, and ethical oversight.