what is the Newton's Method Formula?  Show me a graph how it works!! pleaz.. tell me if there's a case where it will not work!!! thx

Expert Answers

An illustration of the letter 'A' in a speech bubbles

Newton's Formula is used to approximate the root of a function. The formula states that if a function is defined over real x, and f is diffrentiable, then if we start with an initial value x_0, close enough to the root we are looking for, we can approximate x_1 by


The process can be repeated until we reach a satisfactory estimation.


unfortunatly this method does fail sometimes, when the x_n do not converge as needed, one of the reason for it failure can be starting with an intial value that is not close enough to the root. Another reason can be the behavior of the first derivative in the neighboring of the root.

Regarding the graphing you requested, I can not provide it her, but I included a link that shows how the method works.



Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial