Mean Value Theorem (ARC)
Liz Lane-Harvard, University of Central Oklahoma
Deborah Moore-Russo, University of Oklahoma
This ARC provides a pair of activities designed to help students develop an intuitive understanding of the Mean Value Theorem that is grounded in understanding its key foundational ideas (e.g., continuity, average rate of change, instantaneous rate of change). The activities provide opportunities for student engagement with mathematics while also allowing opportunities for collaboration. Active student engagement is promoted through a contextual situation as well as meaningful scaffolding that builds on previous student experience.
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Speed Trap: Introductory Application of the MVT |
This activity is intended to help provide a relatable, real-world scenario for students to begin to use their own experiences to work with average and instantaneous speeds (as related to a speed trap) in order to motivate what the Mean Value Theorem (MVT) means. Following this activity completion, students should have a general idea that a continuous function over a given interval for its domain has at least one point at which the instantaneous rate of change is equivalent to the average rate of change between the two endpoints of the given interval. |
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Mean Value Theorem – Graphical Connections |
This is a predominantly out-of-class scaffolded activity where students further explore the MVT using both algebraic and graphical representations with more emphasis on the slopes of the secant line between the endpoints of the interval in the graphical representations and the slope of tangent lines of certain points on the function in their interval. Particular attention will be given to certain limitations related to continuity and differentiability in the MVT. |
This work is licensed under CC BY-NC-SA 4.0
