Calculus I (MA 111), Fall Quarter, 2000—2001
WorkSheet 5
1) Write the equation of the tangent line to the graph of y = f (x) at the point (3, 4) (note
that this means f (3) = 4)) if f (3) = 6. Write the line using the form which shows the slope
and point.
2) Suppose f (2) = 3 and f (2) = 4.2. Approximate f (2.1), f (2.01), f (1.95). Which probably
gives the best approximation?
3) Suppose that a particle is moving along a horizontal axis in such a way that at time t,
its position is s(t) = t2 − 6t + 8. First draw the horizontal s axis, then answer the following
questions.
a) Where does the particle start? That is, what is s(0)?
b) Is the particle going right or left at time t = 0? Answer in two ways — Þrst plug in a small
positive t value. Then use s (0).
c) What is the particle’s average velocity in the time interval [0, 1]?
d) What is the particle’s average velocity in the time interval [0.5, 1]? in [1, 1.5]?
e) What is the particle’s instantaneous velocity in the time interval at time t = 1? Answer
in two ways — Þrst take a limit and then use the rules of differentiation.
f) What’s so special about the time t = 2?
g) What’s so special about the time t = 3?
h) Describe the motion
4) Suppose that a particle is moving along a horizontal axis in such a way that at time t,
its position is s(t) = −t4 + 2t3 − t + 5. First draw the horizontal s axis, then answer the
following questions.
a) Where does the particle start? That is, what is s(0)?
b) Is the particle going right or left at time t = 0? Answer in two ways — Þrst plug in a small
positive t value. Then use s (0).
c) What is the particle’s average velocity in the time interval [0, 1]?
d) What is the particle’s average velocity in the time interval [0.5, 1], ? in [1, 1.5]?
e) What is the particle’s instantaneous velocity in the time interval at time t = 1? Answer
in two ways — Þrst take a limit and then use the rules of differentiation.
f) At what times is the particle at position s = 0?
g) At what times does the particle change directions?
h) Describe the motion