The transition to undergraduate mathematics has been reported by researchers in Mathematics Education as being a source of many difficulties for many freshmen. In this talk, I will present, from my doctoral research in Mathematics Education, an episode with a pair of students focusing on the concept of differentiability. In the research, I investigated understandings about the concepts of function, limit, continuity and derivative produced by full-time first-year students from UNESP - The State University of Sao Paulo at Rio Claro, Brazil.