1. 3.1 Derivatives

2. Calculus Through the Eyes of Newton
Newton was a realist.
Newton developed Calculus from what he could “see”.
The apple falling from the tree.

3. The Tangent Line Problem
Sketchpad Example

4. Definition of Slope
The slope of a tangent line to a curve at a point x = c is:

5. Example:

6. Example:

7. Example

8. Derivative Notation

9. Derivatives Graphically
The derivative of a function f(x) on some open interval (a, b) represents the collection of points that are the slopes of the original function at every x = c in the interval (a, b).

10. Example:

11. Example

12. Homework
Pg. 124 # 5-9 [3], [5], 38, 39