find the error in this newton-raphson convergence: in matlab

main.m
% Function to find the root using Newton-Raphson method
function root = newtonRaphson(func, derivative, initial_guess, max_iter, tolerance)
    root = initial_guess;   % Initial guess for the root
    old_root = inf;         % Variable to hold the previous estimate
    iter = 0;               % Iteration counter

    % Iterate until convergence or maximum iteration limit is reached
    while abs(root - old_root) > tolerance && iter <= max_iter
        old_root = root;                           % Update the previous estimate

        % Compute the new estimate for the root using Newton-Raphson formula
        root = root - func(root) / derivative(root);

        iter = iter + 1;                            % Increment the iteration counter
    end

    % Check if the method converged or reached the maximum iteration limit
    if iter > max_iter
        disp("Newton-Raphson method did not converge within the maximum number of iterations.");
    else
        disp("Root found successfully using Newton-Raphson method.");
    end
end

% Example usage
f = @(x) x^3 - x - 1;                           % Function
df = @(x) 3 * x^2 - 1;                          % Derivative of the function
initial_guess = 1;                              % Initial guess for the root
max_iterations = 100;                           % Maximum number of iterations
tolerance = 1e-6;                               % Tolerance for convergence

root = newtonRaphson(f, df, initial_guess, max_iterations, tolerance);
error = abs(root - initial_guess);
disp("Error in convergence: " + error);
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