   Chapter 3.8, Problem 31E

Chapter
Section
Textbook Problem

# Explain why Newton’s method fails when applied to the equation x 3 = 0 with any initial approximation x 1 ≠ 0 . Illustrate your explanation with a sketch.

To determine

To Explain:

Why Newton’s method doesn’t work for finding the root of the equation

Explanation

1) Concept:

Use the Newton’s formula for approximation and simplify the expression.

2) Formula:

Newton’s formula for nth approximation:

xn+1=xn-fxnf'xn for n=1,2, 3,

3) Calculation:

f(x) = x3= x1/3

f'(x) = 13 x-2/3

xn+1=xn-fxnf'xn=xn- x

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