Worksheet 2.5 - Rates Of Change And Particle Motion I Worksheet Page 2
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8Calculus Maximus
WS 2.5: Rates of Change & Part Mot I
3. Suppose
M t is the amount of time, in minutes, it takes to boil a cup of water if the water has an
( )
initial temperature of t, degrees Fahrenheit. In a complete sentence, with units, explain the meaning of
each of the following:
( )
=
(a)
M
50
19
−
( )
1
=
(b)
M
19
50
( )
M ′
=
(c)
50
3
( )
′
−
( )
1
=
(d)
M
18
0.2
4. If
g
(v
)
is the fuel efficiency, in miles per gallon, of a car going at v miles per hour,
g v ′ ?
(a) What are the units of
( )
′ g
=
−
(b) In a complete sentence with units, what is the practical meaning of the statement
(
55
)
. 0
54
?
5. Suppose that
C T is the cost of heating your house, in dollars per day, when the temperature outside is
( )
T degrees Fahrenheit.
C ′
= −
(a) Explain in practical terms the meaning of
(23)
0.21
.
C ′
=
= −
(b) If
C
(23) 2.94
and
(23)
0.21
, approximate the cost to heat your house when the temperature
( )
is 20 degrees,
C
20
. Show the work that leads to your answer.
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