# Follow that Car

- Author:
- Jan Mays

- Topic:
- Derivative

A car is travelling down a highway away from its starting location with distance function:
D(t) = 8 (t3 – 6t2 + 12t) miles where t is in hours

1. How far has the car travelled after 1, 2, and 3 hours?
2. Draw a line for each of the following points on the function. What does the slope of each line tell you about the car?
a. t = 0 to t = 1
b. t = 1 to t = 2
c. t = 2 to t = 3
3. Does the car ever stop? Explain your reasoning.
4. What is the average velocity over the intervals
a. t = 1 to t = 3?
b. t = 1.5 to t = 2.5?
c. t = 1.9 to t = 2.1?
5. Use your answers from question 4 to estimate the velocity at t = 2.