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
C x
C x
C
x
+
−
′
≈
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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