   Chapter 2.R, Problem 76E

Chapter
Section
Textbook Problem

# The cost, in dollars, of producing x units of a certain commodity is C ( x ) = 920 + 2 x − 0.02 x 2 + 0.00007 x 3 (a) Find the marginal cost function.(b) Find C'(100) and explain its meaning.(c) Compare C'(100) with the cost of producing the 101st item.

To determine

(a)

To find:

The marginal cost function

Explanation

1. Concept:

Use differentiation

2. Formula:

i. C'x=ddx(Cx)

ii. Power rule:

ddxxn=nxn-1

iii. Sum rule:

ddxfx+gx=ddxfx+ddx(gx)

iv. Constant multiple rule:

ddxCf(x)=Cddx(fx)

v. Difference rule:

ddxfx-gx=ddxfx-ddx(gx)

vi. Constant function rule:

ddxC=0

3. Given:

Cx=920+2x-0.02x2+0.00007x3

4. Calculation:

Marginal cost function is the derivative of cost function with respect to the amount of commodity produced

C'x=ddxCx=ddx(920+2x-0

To determine

(b)

To find:

C'100 and explain its meaning

To determine

(c)

To compare:

C'100 with the cost of producing the 101st item

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