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For which of the initial approximations $ x_1 = a $, $ b $, $ c $, and $ d $ do you thing Newton's method will work and lead to the root of the equation $ f(x) = 0 $?

$a, b,$ or $c$ will likely work

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Derivatives

Differentiation

Volume

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

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04:09

02:35

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05:01

01:48

02:31

04:04

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01:51

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We know that when X one equals d, the tangent line intersects with the X axis far off to the left not particularly close. Therefore, we know that X two intersex the X axis further away to the right. Therefore, we know Newton's method would failed for this initial approximation there for a being C will work. However, we already established why d may not work given New Newton's method.

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