Project 17
MAC 2311
1.
Examine the function
g
(
t
) = 50 + 30(
t

1)
1
/
3
e

t/
6
.
a)
Calculate
g
0
(
t
)
and find its critical numbers.
g
0
(
t
) = 5(
t

1)

2
/
3
e

t/
6
(3

t
)
b)
Do any of the critical numbers that you found in part(b) correspond to horizontal tangent
lines? vertical tangent lines? Which ones?
c)
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?
max is about 73 Fahrenheit when
t
= 3
hours
g)
Around what instant does the room seem to experience the most rapid change in tem
perature? (For this particular function, the answer should already be on your paper–at
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 Spring '08
 ALL
 Critical Point, Max, maximum room temperature, initial room temperature

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