During a sequence of tutorials conducted by the first author, it became evident that students were not seeing how to apply the theorem concerning a continuous function on a closed and bounded interval attaining its extreme values in situations in which it is necessary first to construct the closed and bounded interval by reasoning about properties concerning asymptotes. The paper describes 1 tutorial with 10 students and a follow-up revision session with 2 of the students the same day concerning the use of this theorem in which the tutor used the pedagogic strategy of learner-generated examples. The students' responses and the tutor's observations are analysed using constructs of "example spaces," "structure of attention" and "dimensions of possible variation."