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Project 22
MAC 2311
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1.
Examine the function
g
(
t
) = 50 + 30(
t

1)
1
3
e

1
6
t
.
a)
Calculate
g
0
(
t
).
b)
Find the critical numbers of
g
(
t
).
c)
Do any of the critical numbers that you found in part(b) correspond to
horizontal tangent lines? vertical tangent lines? Which ones?
d)
Find the maximum and minimum value(s) of
g
(
t
) on [0
,
9].
e)
Use a number line to ﬁnd the intervals on which
g
0
(
t
) is positive and
negative. What seems to be the relationship between the sign (+ or

)
of
g
0
(
t
) and the maximum value? Why might this be true (think of
positive/negative slopes)?
f)
Suppose
g
(
t
) represents the temperature (in
◦
F
) of a cold storage room
t
hours after the room is accidently left open. What is the initial room
temperature (to the nearest degree)? What is the maximum room
temperature (to the nearest degree), and after how many hours does it
occur?
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Around what instant does the room seem to experience the most rapid
change in temperature? (For this particular function, the answer should
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 Fall '08
 ALL
 Calculus

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