create a function that performs newton's method without the user inputting the derivative with comments in matlab

main.m
function root = newtonsMethod(f, x0, tol, maxIter)
% Function to perform Newton's method
% Input:
%   f - function handle representing the function for which the root is to be found
%   x0 - initial guess for the root
%   tol - tolerance: algorithm stops if |f(x)| < tol
%   maxIter - maximum number of iterations allowed
% Output:
%   root - root of the function f

% Initialize variables
iter = 0;
x = x0;
diff = tol + 1;

% Perform Newton's method iteration until convergence or max iterations
while (diff > tol) && (iter < maxIter)
    % Evaluate the function and its derivative at x
    fx = f(x);
    fprime = (f(x + tol/1000) - f(x - tol/1000)) / (2*(tol/1000));
    
    % Update x using Newton's method formula
    x = x - fx / fprime;
    
    % Calculate the difference from the previous iteration
    diff = abs(fx);
    
    % Increment the iteration counter
    iter = iter + 1;
end

% Assign the found root
root = x;
end
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main.m
function y = myFunction(x)
% Function f(x) = x^2 - 3

y = x^2 - 3;
end
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main.m
f = @myFunction;
x0 = 2; % Initial guess
tol = 1e-6; % Tolerance
maxIter = 100; % Maximum number of iterations

root = newtonsMethod(f, x0, tol, maxIter);
disp(root); % Display the found root
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