Thread: Newton raphson method

i need to solve this equation with newton raphson method

x^3-3x+1

thank you

By Bolzano's Theorem there is a solution in . Choose and construct the corresponding sequence.

Surely you are not expecting people to do this problem for you. Show what you have done. Of course, Newton-Raphson is an iterative method- for each approximation, , to the solution of f(x)= 0, should be a better approximation and, hopefully, the sequence will converge to a solution.

Originally Posted by HallsofIvy

Surely you are not expecting people to do this problem for you. Show what you have done. Of course, Newton-Raphson is an iterative method- for each approximation, , to the solution of f(x)= 0, should be a better approximation and, hopefully, the sequence will converge to a solution.

maybe i should find the location of the root by the method of tabulation ?

Look at FernandoRevilla's post!

for an equation like this ...

newton raphson iterative scheme is given by



for the given equation f(x)=

first we find the location of the root by the method of tabulation . .

the table for f(x) is

x 0 1 2 3 4
f(x) -4 -13 -12 -1 28

the positive root is near x = 3

we take in newton raphson iterative scheme



we get ,

similarly ,

and




thus , the positive root is 3.0514 , correct to five significant digits