   Chapter 2.6, Problem 40E

Chapter
Section
Textbook Problem

Revenue Of a Travel Agency Suppose that the total revenue realized by the Odyssey Travel Agency is R = f(x) thousand dollars if x thousand dollars are spent on advertising. a. What does f ( b )   −   f ( a ) b − a (0 < a < b) measure? What are the units? b. What does f’(x) measure? Give units. c. Given that f’(20) = 3, what is the approximate change in the revenue if Odyssey increases its advertising budget from $20,000 to$21,000?

a.

To determine

To explain: The value that is measured by f(b)f(a)ba and its unit.

Explanation

The total revenue realized by the Odyssey Travel Agency is,

R=f(x) (1)

Where,

• x is the amount spent on advertising in thousand dollars.
• R is measured in thousand dollars.

The average rate of change of function f over the interval [x,x+h] is,

f(x+h)f(x)h .

The ratio f(b)f(a)ba represents the average rate of change of revenue over the interval [a,b] .

If the advertising budget changes from a thousand dollars to b thousand dollars, then the average rate of change of revenue is f(b)f(a)ba

b.

To determine
The value that is measured by f(x) with units.

c.

To determine
The approximate change in the revenue.

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