newton-raphson iteration in matlab

main.m
x(i+1) = x(i) - f(x(i))/f'(x(i))
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main.m
% Define the function that we want to find the root of
f = @(x) x^3 - 5*x^2 + 6*x - 2;

% Define the first derivative of the function
df = @(x) 3*x^2 - 10*x + 6;

% Set an initial guess for the root
x0 = 1;

% Set a tolerance level for convergence
tol = 10^-6;

% Initialize the error to a high value
err = Inf;

% Loop until the error is below the tolerance level
while err > tol
    % Calculate the next estimate of the root
    x1 = x0 - f(x0)/df(x0);
    
    % Calculate the error between the current and previous estimates
    err = abs(x1 - x0);
    
    % Set the current estimate to be the previous estimate for the next iteration
    x0 = x1;
end

% Output the final estimate of the root
disp(['The root of the function is approximately ', num2str(x1)])
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