% The program uses the Newton Raphson method to estimate a root of the equation 
% f(x)=0. The input parameters are x_1 which is an initial estimate of the root 
% and the tolerance = epsilon with which the root will be estimated.


function [x] = NewtonRaphson(x_1,epsilon)

% With the next command ask for high accuracy (more decimals)

format long

% We give an initial value so that the while loop will get started

x = x_1 ; 

% n will count the number of repetitions needed to achieve the desired
% accuracy.

n=0;   

% The method 

while (abs(fcn(x)) > epsilon)

  x_new = x- fcn(x)/derivfcn(x) % Next estimate of the root.
  
  n=n+1                         % Number of repetitions.   
  
  x=x_new;                      % Set x to be the new estimate in order to calculate again.
  
end