1. Differentiability and Rates of Change

2. To be differentiable, a function must be continuous and smooth. Derivatives will fail to exist at: cornercusp vertical tangent discontinuity (jump)

3. True/False : 1)If a function is differentiable, then it must be continuous. give and example 2) If a function in continuous, then it must be differentiable. give an example

5. 2) 1)

6. Recall the connection between average rate of change an instantaneous

7. Review: average slope: slope at a point: average velocity: (slope) instantaneous velocity: (slope at 1 point) If is the position function: These are often mixed up by Calculus students! So are these! velocity = slope

8. The slope of a curve at a point is the same as the slope of the tangent line at that point. If you want the normal line (perpendicular line), use the negative reciprocal of the slope.

16. 7) 8)