Math 1100
Homework 9
18 September, 2013
Name:
The questions on this quiz are quite similar mathematically to the ones in section 9.9
in your book, but in the context of a physics rather than a financial application. Think
carefully about your interpretations.
Suppose a particle moves along a straight line. The distance it has travelled in feet after
t seconds is given by
p(t) = t3 + 6t2 + 4
1. (4 points) Find p(4). Explain what it represents.
2. (4 points) Find the velocity function v(t).
3. (2 points) Find the velocity of the particle at time t = 4.
4. (2 points) What does you answer to question 3 predict about the motion of the particle
in the next second?
5. (2 points) What does your answer to question 3 predict about the motion of the particle
in the next 4 seconds?
6. (4 points) Find p(5) − p(4). Explain what it represents.
7. (4 points) Find p(8) − p(4). Explain what it represents.
8. (4 points) What do your answers to questions 4–7 tell you about using derivatives to
estimate functions?