   Chapter 4.8, Problem 6E ### 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

# Use Newton’s method with the specified initial approximation x1 to find x3, the third approximation to the root of the given equation. (Give your answer to four decimal places.)2x3 − 3x2 + 2 = 0,    x1 = −1

To determine

To find: The third approximation x3.

Explanation

Formula used:

The Newton’s formula is, xn+1=xnf(xn)f(xn), where f(x) is the given function.

Given:

The initial approximation is x1=1.

The function is f(x)=2x33x2+2.

Calculation:

Calculate the derivative of f(x).

f(x)=ddx(2x33x2+2)=2ddx(x3)3ddx(x2)+ddx(2)=6x26x+0=6(x2x)

Evaluate the value of f(x) at x1=1,

f(1)=6((1)2(1))=6(1+1)=6(2)=12

Calculate the value of f(x) at x1=1,

f(1)=2(1)33(1)2+2=23+2=3

Calculate x2 by using Newton’s method

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

Set n=1, and obtain the value of x2

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In problems 5-8, Use a calculator to evaluate the indicated powers. 8.

Mathematical Applications for the Management, Life, and Social Sciences

#### Evaluate the integral. 8. tsintcostdt

Single Variable Calculus: Early Transcendentals

#### For f(x) = 10x2, f′(3) = _____. 10 20 30 60

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 