how to implement newtons method in matlab

main.m
function [x, iterations] = newton(f, df, x0, tol, maxit)
% Inputs:
%   f: function handle for the function to find roots of
%   df: function handle for the first derivative of f
%   x0: initial guess
%   tol: tolerance for stopping criterion
%   maxit: maximum number of iterations
% Outputs:
%   x: approximation of the root
%   iterations: number of iterations required

% initialize variables
x = x0;
fx = f(x);
iterations = 0;

% loop until stopping criterion is satisfied or maximum iterations reached
while(abs(fx) > tol && iterations < maxit)
    x = x - fx/df(x);
    fx = f(x);
    iterations = iterations + 1;
end
end
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main.m
% define function and derivative
f = @(x) x.^3 - 2*x - 5;
df = @(x) 3*x.^2 - 2;

% call newton function
[x, iterations] = newton(f, df, 2, 1e-6, 100);

% print results
fprintf('Approximate Root: %.6f\n', x);
fprintf('Iterations Required: %d\n', iterations);
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