💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Numerade Educator

Like

Report

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

$$
x_{3}=-1.29172
$$

Discussion

You must be signed in to discuss.

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