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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Suppose that the cost (in dollars) for a company to produce x pain; of a new line of jeans is

C(x) = 2000 + 3x + 0.01x2 + 0.0002x3

(a) Find the marginal cost function.

(b) Find C′(100) and explain its meaning. What does it predict?

(c) Compare C′(100) with the cost of manufacturing the 101 st pair of jeans.

(a)

To determine

To find: The marginal cost function if the cost function is C(x)=2000+3x+0.01x2+0.0002x3.

Explanation

The cost function is C(x)=2000+3x+0.01x2+0.0002x3.

Obtain the derivative of the cost function and obtain the marginal function.

C'(x)=ddx(2000+3x+0

(b)

To determine

To find: The value of C'(100) and interpret it. Explain what it predicts.

(c)

To determine

To compare: The values of C'(100) and the cost of manufacturing the 101st pair of jeans.

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