Section 7.1
Name:
Pd:
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You must show your work for all calculations using proper notation
at all times to receive full credit.
1. Let f be a continuous function whose graph is shown to the left, and
x
let h( x) 
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 f (t )dt
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(a) Find the zeros of h. Justify your answer.
(b) On what interval is h increasing? Show the analysis that leads to
your answer.
(c) What is h(0)?
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2. (no calculator) A particle moves along the x-axis so that its velocity at any time t≥0 is given by
v(t) = 3t2 – 2t – 1. The position x(t) is 5 for t = 2.
a) Write a polynomial expression for the position of the particle at any time t≥0.
b) For what values of t, 0≤t≤3, is the particle’s instantaneous velocity the same as its average velocity on the
closed interval [0,3].
c) Find the total distance traveled by the particle from time t = 0 until time t = 3.
3. From 1970 to 1980, the rate of potato consumption in a given country was C(t) = 2.2 + 1.1t millions of
bushels per year, with t being years since January 1, 1970. How many bushels were consumed between
January 1, 1975 and December 31, 1979?
4. A car travels along a straight road for 30 seconds starting at time t=0. Its acceleration, in ft/sec2, is given
by the linear graph below, for 0<t<30. At t=0, the velocity of the car is 0 and its position is 12.
(a) What is the velocity of the car when t=6? Indicate units of
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measure.
(b) At what time t does the car reach its maximum velocity?
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Justify your answer.
(c) What is the position of the car when t=18?
(d) What is the total distance the car travels in this 30 second
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interval? Justify your answer.
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