Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Explain why Newton's method doesn't work for finding the root of the equation$$ x^3 - 3x + 6 = 0 $$if the initial approximation is chosen to be $ x_1 = 1 $.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Tyler Gaona

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Derivatives

Differentiation

Volume

Missouri State University

Campbell University

Harvey Mudd College

Lectures

04:35

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

06:14

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

08:50

Explain why Newton's …

00:47

0:00

01:16

06:17

Newton's method fails…

02:14

explain why Newton's method fails to find the roots of the equation. F of X equals zero, where FX is X cubed minus three x plus six. If we used the initial approximation, X one is equal to one. Answer this question. We should recall. Recall what Newton's method means geometrically. Let me just draw the graph of function and suppose that we want to find on approximation to this route here. What we would do is just choose a nearby point on the X axis and draw the tangent line to the graph of our function. At that point, no, we would do is see where the tangent line intersex the X axis again, and we'LL use that as our next approximation, and we'LL keep repeating this process until we are as close to the route as we like. So now if you write down the equation for this tangent lines, he were intersects the X axis. You can find the formula for the next approximation for Newton's method. So the way we get our next approximation as we take our current approximation except Ben and we subtract F of X have been divided by F prime of exhibition So to use this formula, say we want to find the next approximation, we would have to find the derivative. So let's compute the derivative. We use the power rule. We get that the derivative is three X squared minus three. All right, and now let's see what would happen to find X up to. We would need to compute f prime of X of one. So let's do that. We're given in the initial approximation is one. And now if we plug that in death prime, we just get three minus three, which is zero. Okay, and now we see where the problem is. We don't we're not able to find the next approximation because dividing by zero is not defined. So what's happening geometrically, let's say that here on the X axis is X one. And now, in this situation, since F prime of X one is zero, we have something that could possibly look like this. The point is that the tangent line at this point has slope zero, so it's horizontal, and that means that it will never cross the X axis again. So that's why we can't use this point to find the next approximation for Newton's method

View More Answers From This Book

Find Another Textbook

05:57

Find an appropriate parametrization for the given piecewise-smooth curve in …

03:26

Solve fbr X :3-5x = 34+x

02:44

Evaluate the integral by interpreting it in terms of areas_ [S(2- + V 81 dx<…

01:58

Convert the polar equation to rectangular form.r=6cos20

02:18

49. 3X1 6x2 ~9 2x1 4x2 6

02:36

Does college major depend on whether you are a athlete r not? A survey asks …

06:21

Decision tree classification: Consider the following instancesInstance

01:30

12. Which of the following defines the interval of real numbers [-4, 2] ? …

01:50

Evaluate the following integrals: 20r"dr(b)K edx

03:14

Evaluate the iterated integral by converting to polar coordinates_ a2 y2 Y d…