% f(x) = x^3 − 9x^2 + 3.8197
% f'(x) = 3x^2 − 18x
 
% Define functions
func = @(x) x.^3 - 9*x.^2 + 3.8197;
diff_func = @(x) 3*x.^2 - 18*x;
 
% Random initial guess
x = rand();
fprintf('x_0 = %.4f\n', x);
 
% Table header
fprintf('%-3s %-12s %-12s %-12s %-12s\n', ...
    'n','x_i','f(x)','f''(x)','|x_(i+1)-x_i|');
 
% Newton iterations
for count = 1:5
    fx = func(x);
    dfx = diff_func(x);
    next_x = x - fx/dfx;
    fprintf('%-3d %-12.6f %-12.6f %-12.6f %-12.6f\n', ...
        count, x, fx, dfx, abs(next_x-x));
    x = next_x;
end
 

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