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**The MVT and the FTC** – This presentation begins with a classroom exercise that will lead into the Mean Value Theorem. Then we will consider the theorems leading up to the MVT and the proof of the MVT, the graphical interpretation of the MVT, AP Calculus Exam question about the MVT, how the MVT is used to prove the Fundamental Theorem of Calculus, and using the FTC on the AP Exams Have your graphing calculator handy. (AB and BC)

**PowerPoint Slides for both parts: **From the MVT to the FTC

**Videos of Presentation**

To be posted soon

**From the MVT to the FTC – part 1: MVT**

**From the MVT to the FTC – part 2: FTC**

**2019 CED Topics **5.1, 6.4, 6.7, 6.8

- Discovering the MVT and Foreshadowing the MVT
- Fermat’s Penultimate Theorem
- Rolle’s Theorem
- The Mean Value Theorem 1 and
- The Mean Value Theorem 2
- Working Towards Riemann Sums
- Riemann Sums
- The Definition of the Definite Integral
- Foreshadowing the FTC
- The Fundamental Theorem of Calculus
- More About the FTC
- Y the FTC?

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