## Using the Derivative

**Applications of the Derivative**

**Related Rate Examples**

**Drills on using the Mean Value Theorem**

**Newton's Method**

**2006 Related Rate Projects (PowerPoint)**

**Download a TI-83 Program for**

**Newton's Method**

**(Requires GraphLink software)**

**AP Calculus (BC) Topics**

I.

**Functions, Graphs and Limits**

D.

**Continuity as a property of functions.**

- Understanding continuity in terms of limits.
- Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and Extreme Value Theorem).

**Derivatives**

E.

**Applications of derivatives.**

- Analysis of curves, including the notions of monotonicity and concavity.
- Optimization, both absolute (global) and relative (local) extrema.
- Modeling rates of change, including related rates problems.
- Use of implicit differentiation to find the derivative of an inverse function.
- Interpretation of the derivative as a rate of change in varied applied contexts, including velocity, speed, and acceleration.