  Beyond the difficulty to give true practical motives to introduce a theorem,
the didactic transposition of scholarly knowledge in a school setting often
leads to freezing a technical tool into a theorem given under minimal
assumptions. Probably whole categories of exercises have no other justification
than establishing the necessity of introducing a theorem under minimal
assumptions in a curriculum. The mean value theorem represents a paradigmatic
situation, showing not only the expectations of the curriculum writers, but
also part of the school unconscious that manifests itself in the very notion of
rigor.
