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MATH 110 BUSINESS CALCULUS
CHAPTER 3 INTRODUCTION TO THE DERIVATIVE
Section 3.8 The First Application: Marginal Analysis
C(x)
is a Cost Function
R(x)
is a Revenue Function
P(x)
is a Profit Function
P(x) = R(x) – C(x)
Marginal Cost, Revenue, and Profit functions
C’(x)
is the Marginal Cost Function
R’(x)
is the Marginal Revenue Function
P’(x)
is the Marginal Profit Function
P’(x) = R’(x) – C’(x)
Interpretation:
(1
)
(
)
()
1
Cx
+−
′
≈
A Marginal Cost is an approximate cost of one more item.
The analogous interpretation applies to a Marginal
Revenue and a Marginal Profit.
So, a Marginal Revenue is an approximate revenue from
the sale of one more item.
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View Full Document Average Cost, Revenue, and Profit functions
()
Cx
x
=
is the Average Cost
Rx
x
=
is the Average Revenue
P x
Px
x
=
is the Average Profit
Example: Marginal cost and Average Cost
The cost of producing x teddy bears per day at the
Cuddly Companion Co. is calculated by their marketing
staff to be given by the formula
2
( )
100
40
0.001
x
x
=+
−
a. Find the marginal cost function and use it to estimate
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This note was uploaded on 10/19/2011 for the course MATH 110 taught by Professor Staff during the Spring '11 term at S.F. State.
 Spring '11
 Staff
 Calculus, Derivative

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