   Chapter 2.7, Problem 53E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

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 f(x) and its units.

Explanation

The function f(x) is the cost of production.

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 f(x) is the instantaneous rate of change of C with respect to x,

The derivative f(x) is rate of change of the production cost with respect to the number of ounces of gold produced

(b)

To determine

The meaning of f(800)=17.

(c)

To determine

To check: Whether the derivative f(x) will increase or decrease for short term and also for long term.

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