Chapter 2.7, Problem 53E

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8th Edition

James Stewart

ISBN: 9781305270343

Textbook Problem

The cost of producing *x* ounces of gold from a new gold mine is *C* = *f*(*x*) dollars.

(a) What is the meaning of the derivative *f'*(*x*)? What are its units?

(b) What does the statement *f'*(800) = 17 mean?

(c) Do you think the values of *f'*(*x*) will increase or decrease in the short term? What about the long term? Explain.

(a)

To determine

The meaning of derivative

Explanation

The function

The cost of production is depends on number of ounces of gold produced.

That is, the cost of production is a function of ounces of gold produced.

Note that, the derivative *C* with respect to *x*,

The derivative

(b)

To determine

The meaning of

(c)

To determine

**To check:** Whether the derivative

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