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Brief Applied Calculus
5
th
ed
Berresford & Rockett
SOC Exam 2 Review O’Brien
F09
1
Survey of Calculus Exam 2 Review:
3.3 – 4.4
Show all
of your support work on all problems.
Section 3.3
1.
Without using a calculator, find the absolute extreme values of each function on the given interval.
a.
()
1
8x
2x
4x
x
f
2
3
+
−
+
=
on [2, 1]
b.
( )
1
18x
x
x
g
2
4
+
−
=
on [4, 4]
2.
The fuel economy (in miles per gallon) of an average American midsized car is
( )
48.7
1.28x
.02x
x
E
2
+
+
−
=
, where
x is the driving speed (in miles per hour, 20
≤
x
≤
60).
At what speed is fuel economy greatest?
3.
An opentop box is to be made from a square piece of cardboard that measures 12 inches on each side by cutting a
square from each corner and folding up the sides.
What are the dimensions and volume of the largest box that can be
made in this way?
4.
A company wants to build a parking lot along the side of one of its buildings using 996 ft of fence.
If the side along
the building needs no fence, what are the dimensions of the largest possible parking lot?
5.
Giddings Gizmos finds that it costs $60 to produce each gizmo, and that its fixed costs are $120 per day.
The price
function is p(x) = 520 – 10x, where p is the price (in dollars) at which exactly x gizmos will be sold.
Find the quantity
Giddings should produce and the price it should charge to maximize profit.
Also find the maximum profit.
Section 3.4
6.
An automobile dealer can sell 14 cars per day at a price of $19,000.
He estimates that for each $150 price reduction,
he can sell 3 more cars per day.
If each car costs him $16,700 and his fixed costs are $1000, what price should he
charge to maximize profit?
How many cars will he sell at this price?
[Hint:
Let x = the number of $150 price
reductions.]
7.
A manufacturer wants to design an open box that has a square base and a volume of 864 cubic inches.
Find the
dimensions of the box that can be made with the smallest amount of material.
8.
An orange grower finds that if she plants 43 trees per acre, each tree will yield 27 bushels of oranges.
She also
estimates that for each additional tree that she plants per acre, the yield of each tree will decrease by 3 bushels.
How many trees should she plant per acre to maximize her harvest?
9.
A farmer with 800 feet of fence wants to enclose a rectangular field and then
divide it into four plots, as in the diagram.
What should be the dimensions of
each enclosure if the total area is to be maximized?
What is the maximum area
that can be enclosed?
10.
A homeowner wants to build a 5000 square foot fencedin garden along her driveway.
If the fence along the driveway
costs $6 per foot, while on the other three sides, the fence costs $2 per foot, what dimensions will minimize the cost of
the fence?
What is the minimum cost?
11.
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 Spring '09
 crespo
 Calculus

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