%% Cuencas de convergencia

close all
clc
clear

% gamma = 2;
% f = @(x) abs(x).^gamma;
% df = @(x) gamma.*abs(x).^(gamma-1).*sign(x);


f = @(x)  (x+3).*(x-1).*(x-4);%x.^3 - 2*x.^2 - 11*x + 12; % = (x+3)*(x-1)*(x-4)
df = @(x) 3*x.^2 - 4*x - 11;
x = 2.354; % 2.352, 2.353, 2.354
xprev = inf;


% x = 2;
% xprev=inf;

plot(linspace(-4,5), f(linspace(-4,5)))
hold on
plot(linspace(-4,5), 0*linspace(-4,5), '--k')
hold on
plot(x,f(x), 'ok', 'MarkerSize', 4, 'MarkerFaceColor', 'k')

n_Newton = 0;
x_Newton = [x];

while abs(x - xprev) > 1e-3*abs(x)
    xprev = x;
    x = x - f(x)/df(x);
    pause
    plot(x,f(x), 'ok', 'MarkerSize', 4, 'MarkerFaceColor', 'k')
    n_Newton = n_Newton + 1;
    x_Newton = [x_Newton; x];
end

n_Newton
x_Newton