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CALCULUS AP – Review Chapter 4.4 to 4.6
1)
What is the smallest perimeter possible for a rectangle whose area is to be 40 square meters?
8 10 m
2)
You are planning to make an open rectangular box from a 38 by 44 in. piece of cardboard by cutting congruent
squares from the corners and folding up the sides.
(a)
What are the dimensions of the box of largest volume that you can make this way?
[ ]
6.779 24.443 30.443 in
×
×
(b)
What is its volume?
3
5044.006 in
3)
Suppose the revenue, in dollars, for producing
x
skateboards is given by
( )
120
R x
x
=
and the cost to produce the
skateboards is given by
3
2
( )
0.0002
0.4
70
4000
C x
x
x
x
=
−
+
+
.
Find the production level to the nearest skateboard that
will maximize profit.
(
Profit = Revenue – Cost
)
[ ]
1393
4)
Find the linearization
( )
L x
of
2
( )
2
5
10
f x
x
x
= −
+
+
at
7
x
=
.
[ ]
( )
23
108
L x
x
= −
+
5)
If
2
( )
4
4
11
f x
x
x
=
−
−
,
(a)
find the linearization
L
(
x
) at
3
x
= −
, and
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 Spring '09
 Zalla

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