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Applied Calculus for the Manageria...

10th Edition
Soo T. Tan
ISBN: 9781285464640
Textbook Problem

Demand for Tents The demand function for Sportsman 5 × 7 tents is given by

P = f(x) = −0.1x2x + 40

where p is measured in dollars and x is measured in units of a thousand.

  1. a. Find the average rate of change in the unit price of a tent if the quantity demanded is between 5000 and 5050 tents, between 5000 and 5010 tents.
  2. b. What is the rate of change of the unit price if the quantity demanded is 5000?

a.

To determine
The average rate of change in the unit price of the tent.

Explanation

Given:

The demand function for sportsman 5×7 tents is,

f(x)=0.1x2x+40 (1)

Where,

  • f(x) is measured in dollars.
  • x is measured in units of thousand.

Definition used:

The average rate of change of function over the interval is,

f(x+h)f(x)h (2)

Calculation:

Substitute x+h for x in equation (1),

f(x+h)=0.1(x+h)2(x+h)+40=0.1(x2+2xh+h2)xh+40=0.1x20.2xh0.1h2xh+40

Substitute 0.1x20.2xh0.1h2xh+40 for f(x+h) and 0.1x2x+40 for f(x) in equation (2),

f(x+h)f(x)h=0.1x20.2xh0.1h2xh+40(0.1x2x+40)h=0

b.

To determine
The rate of change of the unit price.

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