Based on the theoretical elements of the instrumental approach to tool use known as Task-Technique-Theory (Artigue, 2002), this paper analyses and discusses the performance of graduate students enrolled in a Teacher Training program. The latter performance relates to tracing tangent lines to the curve of a quadratic function in Dynamic Geometry Software, within the context of the Mean Value Theorem. The purpose of the paper is to show how usage of Dynamic Geometry can be helpful in promoting production of techniques and theory in the context of the Theorem, based on its geometric interpretation. The results illustrate the pragmatic and epistemic role of the Dynamic Geometry Technique.