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Explain why Newton's method fails when applied to the equation $ \sqrt[3]{x} = 0 $ with any initial approximation $ x_1 \not= 0 $. Illustrate your explanation with a sketch.

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Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Derivatives

Differentiation

Volume

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

03:31

If $ f(x) = \left\{

0:00

If$$f(x)=\left\{\b…

04:41

Newton's method fails…

05:08

00:47

Explain why Newton's …

06:17

question 33. We're looking at our function as extra 1/3 but a key root of X and a prime of X and, of course, is 1/3 x to the negative 2/3. So x to the n plus one is an equal x minus x to the 1/3 over 1/3 X to the negative 2/3. So simplify that I would have, um, one there x to the to certain so back to the I'm just simply crying this part right here, x and we're when they're x 2/3 I'm going to invert and multiply, So I'm gonna have X to the 1/3 times three x to the 2/3 over one. So I'm just gonna multiply them when I must play and the exponents. So I have three x. So now I have X minus three X, which gives me and negative to X and negative X will not converge

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