Chapter 3.8, Problem 31E

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

Chapter
Section

### Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

# Advertising Costs A company that produces digital audio players estimates that the profit for selling a particular model is P = − 76 x 3 + 4830 x 2 − 320 , 000 ,             0 ≤ x ≤ 60 where P is the profit in dollars and x is the advertising expense in 10,000s of dollars (see figure). Use Newton's Method to approximate the smaller of two advertising amounts that yield a profit of $2,500,000. To determine To calculate: Approximation of smaller of two advertising amounts that yield a profit of$2,500,000 by using Newton’s Method when the company producing digital audio players estimates that the profit for selling a particular model is P=76x3+4830x2320000,0x60, where P is the profit and x is the advertising expense in 10,000s of dollars.

Explanation

Given:

P=76x3+4830x2320000,0x60

Refer the image in the given question.

Formula used:

xn+1=xnf(xn)f'(xn)

Calculation:

Given function is,

P=76x3+4830x2320000……..(1)

Plug the profit given for P,

2500000=76x3+4830x2320000

Initial guess of x=20

Solve using Newton’s Method, keep doing until a constant value is reached.

The Newton’s Formula is

xn+1=xnf(xn)f'(xn)

We have to approximate the fixed point of f

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