The function f(x) = x1/3 is not differentiable at x = 0. Show that Newton’s Method fails to converge using   x1 = 0.1.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
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The function f(x) = x1/3 is not differentiable at x = 0. Show that Newton’s Method fails to converge using   x1 = 0.1.

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Step 1

Given:

The function fx=x13 is not differentiable at x=0.

We have to show that the Newton's method fail to converge using x1=0.1.

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