Problem

Use Newton's method with initial approximation $ …

00:54

Problem 8 Easy Difficulty

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 $

Answer

$$
x_{3}=-1.29172
$$

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

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Problem 42

Video Transcript

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

Amrita B.

Topics

Derivatives

Differentiation

Volume

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Top Calculus 2 / BC Educators

Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University