Classwork V
Sections 3.1, 3.2
Prove that there is no line through the point (1
,
5) that is tangent to
y
= 4
x
2
. (Leithold
2.1.49).
Compute the following using the deﬁnition of the derivative:
•
d
d
x
(2
x

1) =
•
d
d
x
(
x
3
)
=
•
D
x
(
x
2

x
)
=
•
f
0
(2) where
f
(
x
) =
2
x

1
.
•
d
g
d
x
where
g
(
x
) =
√
3
x
. (3.2.19).
Suppose that the revenue
R
(
n
) in dollars from producing
n
computers is given by
R
(
n
) =
.
4
n

.
001
n
2
. Find the instantaneous rates of change of revenue when
n
= 10 and
n
= 100.
(The instantaneous rate of change of revenue with respect to the amount of product pro
duced is called the
marginal revenue
.) (3.1.20).
Suppose a vendor selling turnips at a street fair oﬀers a discount for quantity, so that the
average cost per turnip when buying
n <
30 turnips is
C
(
n
) = 4

.
1
n
. Find the marginal
cost (the instantaneous rate of change of cost – note change of cost not change of average
cost) when
n
= 10 turnips.
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 Summer '08
 Any
 Calculus, Derivative, Continuous function, instantaneous rate, vendor selling turnips, dx ·Dx x2

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