Bc Practice Examination 1 Worksheet Page 9
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10Be Practice
Examination
1
611
SECTION II
Part A
TIME: 30
MINUTES
2 PROBLEMS
A graphing calculator
is
required for
some
of
these problems.
See instructions on
page 4.
t (months)
7
1. A functionjis
defined on the interval
[0,4],
and
its
derivative is
!'
(x)
=
e
SiIU
-
2 cos
3x.
(a)
Sketch!,
in the window [0,4]
x
[-2,5].
(Note that the following
questions
refer to
f)
(b) On what interval isjincreasing?
(c) At
what
value(s) of
x
doesjhave
local
maxima?
Justify your
answer.
(d) How
many points
of inflection
does
the graph
ofjhave?
Justify
your answer.
2. The rate of
sales
of a new software product
is
given
by
S(t),
where S
is
measured in
hundreds of units per
month
and t
is
measured in
months
from the initial release date
of January
1,2012.
The software
company
recorded these
sales
data:
Set) (IOOs/month)
6.12
(a)
Using
a trapezoidal approximation, estimate the number of units the company sold
during the
second
quarter (April
1,
2012, through June
30,
2012).
(b)
After
looking at these
sales
figures,
a manager
suggests
that
the
rate
of
sales
can
be modeled by assuming that the rate to be
initially
120 units/month and to double
every 3
months.
Write an equation
for
S based on
this
model.
(c) Compare the model's prediction for total second quarter sales with your estimate
from
part a.
(d) Use the
model
to predict the average value of
S(t)
for
the
entire first year. Explain
what
your answer
means
.
•
END OF PART
A,
SECTION /I
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