function [rk, k] = newtons_method(f, fp, r0, tol, kMAX)

ratio = 2.0*tol;
k = 0;
rk = r0

x = linspace(-2.5,5,10001);

plot(x,f(x),'--')
hold on

while k < kMAX && abs(ratio) > tol
    F = f(rk);
    Fp = fp(rk);
    ratio = F/Fp
    rkp1 = rk - ratio;
    
    grid on
    plot(rk,0,'.k', 'LineWidth', 2)
    plot(rk,F,'xr', 'LineWidth', 1.2)
    pause(0.5);
    
    rk = rkp1
    k = k+1
end

hold off