1. Applications of derivatives

2. Increasing/Decreasing

3. Increasing: When the slope of the tangent line is positive. Decreasing: When the slope of the tangent line is negative.

4. Points of Inflection

5. A point when the value of the second derivative changes signs

6. Extreme Value Theorem

7. If a function is continuous on the interval [a,b] there exist numbers c and d in [a,b] such that: or f(c) ≤ f(x) ≤ f(d)

8. Position, Velocity, Acceleration

9. If you are given the position function then you can find the velocity function by taking the first derivative and the acceleration by taking the second derivative.

10. Characteristics of Graphs

11. Using the first and second derivative of graphs, you can find characteristics of the original graph such as when it is increasing/decreasing, local maxs/mins, concavity intervals, and points of inflection.