ܥ(1000) = 0.097(1000) + 1.32 = $98.32
.
c.
The total cost of producing 1001 cups is
ܥ(1001) = 0.097(1001) + 1.32 = $98.42
.
d.
The marginal cost of producing 1001
st
cup is
ܥ(1001) − ܥ(1000) = $98.417 − $98.32 = $0.010 ݎ 10 ܿ݁݊ݐݏ
.
e.
The slope of
ܥ(ݔ) = 0.097ݔ + 1.32
is 0.097, so the marginal cost is $0.097, which is about
9.7 cents.
Section 3.4 Quadratic Functions
Without graphing determine whether the parabola opens upward or downward (See Example
1)
3)
ℎ(ݔ) = −3ݔ
ଶ
+ 14ݔ + 1
the parabola opens downward since
ܽ = −3 < 0
.
5)
݃(ݔ) = 2.9ݔ
ଶ
− 12ݔ − 5
the parabola opens upward since
ܽ = 2.9 > 0
Section 3.5 Applications of Quadratic Functions
1)
Business
Carol Bey makes and sells candy. She has found that the cost per box for
making
ݔ
boxes of candy is given by

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5
ܥ(ݔ) = ݔ
ଶ
− 40ݔ + 405
a)
How much does it cost per box to make 15 boxes? 18 boxes? 30 boxes?
b)
Graph the cost function
ܥ(ݔ)
, and mark the points corresponding to 15, 18 and 30
boxes.
c)
What point on the graph corresponds to the number of boxes that will make the cost
per box as small as possible?
d)
How many boxes should she make in order to keep the cost per box at a minimum?
What is the minimum cost per box?