Pauls Online Notes
Pauls Online Notes
Home / Calculus I / Applications of Derivatives / Newton's Method
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 4-13 : Newton's Method

For problems 1 & 2 use Newton’s Method to determine \({x_{\,2}}\) for the given function and given value of \({x_0}\).

  1. \(f\left( x \right) = {x^3} - 7{x^2} + 8x - 3\), \({x_{\,0}} = 5\) Solution
  2. \(f\left( x \right) = x\cos \left( x \right) - {x^2}\), \({x_{\,0}} = 1\) Solution

For problems 3 & 4 use Newton’s Method to find the root of the given equation, accurate to six decimal places, that lies in the given interval.

  1. \({x^4} - 5{x^3} + 9x + 3 = 0\) in \(\left[ {4,6} \right]\) Solution
  2. \(2{x^2} + 5 = {{\bf{e}}^x}\) in \(\left[ {3,4} \right]\) Solution

For problems 5 & 6 use Newton’s Method to find all the roots of the given equation accurate to six decimal places.

  1. \({x^3} - {x^2} - 15x + 1 = 0\) Solution
  2. \(2 - {x^2} = \sin \left( x \right)\) Solution