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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?