Math 122 Review 2
1.
The cost (in dollars) of producing
x
units of a certain commodity is
C
(
x
) =
5000 + 10
x
+ 0
.
05
x
2
.
a. Find the average rate of change of
C
with respect to
x
when the production level
is changed from
x
= 100 to
x
= 105.
b.
Find the instantaneous rate of change of
C
with respect to
x
when
x
= 100.
Explain your answer.
2.
The price in dollars of a house during a period of mild inflation is described by
the formula
P
(
t
) = 85000
e
0
.
04
t
, where
t
is the number of years after 1995.
a. What is the value of the house in the year 2005?
b. At what rate will the value of the house be increasing in the year 2005?
c. When will the value of the house be increasing at a rate of $4000 per year?
1
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2
3.
Let
T
(
t
) be the temperature (in
◦
F) in Dallas
t
hours after midnight on June 2,
2001. The table shows values of this function recorded every two hours.
t
0
2
4
6
8
10
12
14
T
(
t
)
73
73
70
69
72
81
88
91
a. Estimate
T
0
(10). Give units.
b. What is the practical meaning of your answer in (a)?
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 Spring '08
 KUSTIN
 Derivative, Rate Of Change, Mathematical analysis, Convex function

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