create a function that performs newton in matlab

main.m
function [root, iterations] = newtonMethod(f, f_prime, x0, epsilon, max_iterations)
    % Newton's method algorithm
    % Inputs:
    % - f: function handle representing the equation to solve
    % - f_prime: function handle representing the derivative of f
    % - x0: initial guess
    % - epsilon: tolerance for the root approximation
    % - max_iterations: maximum number of iterations
    % Outputs:
    % - root: approximation of the root
    % - iterations: number of iterations performed

    iterations = 0;  % initialize iteration counter
    x = x0;  % initialize iteration value

    while abs(f(x)) > epsilon && iterations < max_iterations
        x = x - f(x) / f_prime(x);  % Newton's method update
        iterations = iterations + 1;  % increment iteration counter
    end

    root = x;  % approximate root
end
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