Problem

For which of the initial approximations $x_{1}=a,…

Problem 4 Easy Difficulty

For each initial approximation, determine graphically what happens if Newton's method is used for the function whose graph is shown.
$$\begin{array}{ll}{\text { (a) } x_{1}=0} & {\text { (b) } x_{1}=1 \quad \text { (c) } x_{1}=3} \\ {\text { (d) } x_{1}=4} & {\text { (e) } x_{1}=5}\end{array}$$

Answer

(a) Newton's method fails
(b) Newton's method fails
(c) Newton's method fails
(d) Newton's method fails
(e) Newton's method works

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Calculus 1 / AB

Essential Calculus Early Transcendentals

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 6

Newton's Method

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Video Transcript

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