Problem

Use Newton's method to approximate the given numb…

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Problem 10 Easy Difficulty

Use Newton's method with initial approximation $ x_1 = 1 $ to find $ x_2 $, the second approximation to the root of the equation $ x^4 - x - 1 = 0 $. Explain how the method works by first graphing the function and its tangent line at $ (1, -1) $.

Name: use newtons method with initial approximation x_1 1 to find x_2 the second approximation to the ro 2
Uploaded: 2019-11-29
Duration: 41 s
Channel: Numerade
Description: Use Newton's method with initial approximation $ x_1 = 1 $ to find $ x_2 $, the second approximation to the root of the equation $ x^4 - x - 1 = 0 $. Explain how the method works by first graphing the function and its tangent line at $ (1, -1) $.

Answer

$$
x_{2}=\frac{4}{3} \approx 1.333
$$

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Discussion

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Video Transcript

The first thing we can do is differentiate the equation being given toe end up with four X cubed minus one. Now use an equation except to his ex of one minus F of X Juan over f prime of X ones. This is why we different cheated above, which is 4/3 which is 1.33 Therefore, we can graft us to look like this.

Amrita B.

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Problem

Use Newton's method to approximate the given numb…

Problem 10 Easy Difficulty

Use Newton's method with initial approximation $ x_1 = 1 $ to find $ x_2 $, the second approximation to the root of the equation $ x^4 - x - 1 = 0 $. Explain how the method works by first graphing the function and its tangent line at $ (1, -1) $.

Answer

$$
x_{2}=\frac{4}{3} \approx 1.333
$$

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Anna Marie V.

Heather Z.

Kayleah T.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Anna Marie V.

Heather Z.

Kayleah T.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Problem

Use Newton's method to approximate the given numb…

Problem 10 Easy Difficulty

Use Newton's method with initial approximation $ x_1 = 1 $ to find $ x_2 $, the second approximation to the root of the equation $ x^4 - x - 1 = 0 $. Explain how the method works by first graphing the function and its tangent line at $ (1, -1) $.

Answer

$$x_{2}=\frac{4}{3} \approx 1.333$$

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Anna Marie V.

Heather Z.

Kayleah T.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Anna Marie V.

Heather Z.

Kayleah T.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

$$
x_{2}=\frac{4}{3} \approx 1.333
$$