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Use Newton's method with the specified initial approximation $ x_1 $ to find $ x_3 $, the third approximation to the root of the given equation. (Give your answer to four decimal places.)

$ x^7 + 4 = 0 $, $ x_1 = -1 $

$$x_{3}=-1.29172$$

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Derivatives

Differentiation

Volume

Missouri State University

Harvey Mudd College

University of Nottingham

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The first thing we're gonna want to do is find the derivative of what we've been given. We're just gonna be seven x the sex. Which means that when x one is negative one, the X two is negative. One minus negative. One to the seventh plus four over seven times negative 16 which gives us access to is negative 1.4 two, which gives us Exit three is negative. 1.42 minus negative, one point for two to the seventh post. Four over 70 native, one point for two to the sex and continuing onwards. We got negative 1.29 17

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