   Chapter 4.8, Problem 10E ### 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 initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 1 = 0. Explain how the method works by first graphing the function and its tangent line at (1, −1).

To determine

To find: The second approximation x2.

Explanation

Formula used:

The newton’s formula is,xn+1=xnf(xn)f(xn)

Given:

The initial approximation is x1=1.

The function is f(x)=x4x1.

Calculation:

Calculate the derivative of f(x).

f(x)=ddx(x4x1)=2ddx(x4)ddx(x)ddx(1)=4x310=4x31

The value of f(x) at x1=1 is,

f(1)=4(1)31=4×11=3

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

f(1)=(1)411=12=1

Calculate x2 by using Newton’s method

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