clear,clc,close all
% Caso convergente, pendiente positiva
a=0;b=1;
g=@(x)0.5*x.^2+0.3;
x0=0.95;
xx=linspace(a,b);
plot(xx,g(xx),'r-'), hold on
plot([a b],[a b],'k-')
axis([a,b,a,b])
set(gca,'XTick',[],'YTick',[])
hold on
title('CASO CONVERGENTE: 0 < g''(x) < 1','Fontsize',16,'Fontweight','b')
x1=g(x0);
plot([x0 x0],[0 x1])
text(x0+0.01,0.03,['x_',num2str(0)],'Fontsize',16,'Fontweight','b')
pause
for i=1:5
    plot([x0 x1],[x1 x1])
    text(x1+0.01,0.03,['x_',num2str(i)],'Fontsize',16,'Fontweight','b')
    text(x1,0,'I','Fontsize',16,'Fontweight','b')
    pause
    x0=x1;x1=g(x0);
    plot([x0,x0],[x0 x1])
    pause
end

clear,clc,close all
% Caso convergente, pendiente negativa
a=0;b=1;
g=@(x)-0.5*x.^2+0.7;
x0=0.95;
xx=linspace(a,b);
plot(xx,g(xx),'r-'), hold on
plot([a b],[a b],'k-')
axis([a,b,a,b])
set(gca,'XTick',[],'YTick',[])
hold on
title('CASO CONVERGENTE: -1 < g''(x) < 0','Fontsize',16,'Fontweight','b')
x1=g(x0);
plot([x0 x0],[0 x1])
text(x0+0.01,0.03,['x_',num2str(0)],'Fontsize',16,'Fontweight','b')
pause
for i=1:5
    plot([x0 x1],[x1 x1])
    text(x1+0.01,0.03,['x_',num2str(i)],'Fontsize',16,'Fontweight','b')
    text(x1,0,'I','Fontsize',16,'Fontweight','b')
    pause
    x0=x1;x1=g(x0);
    plot([x0,x0],[x0 x1])
    pause
end

clear,clc,close all
% Caso divergente, pendiente positiva
a=0;b=1;
g=@(x)1.3*x.^2-0.1;
x0=0.83;
xx=linspace(a,b);
plot(xx,g(xx),'r-'), hold on
plot([a b],[a b],'k-')
axis([a,b,a,b])
set(gca,'XTick',[],'YTick',[])
hold on
title('CASO DIVERGENTE: g''(x) > 1','Fontsize',16,'Fontweight','b')
x1=g(x0);
plot([x0 x0],[0 x1])
text(x0+0.01,0.03,['x_',num2str(0)],'Fontsize',16,'Fontweight','b')
pause
for i=1:5
    plot([x0 x1],[x1 x1])
    text(x1+0.01,0.03,['x_',num2str(i)],'Fontsize',16,'Fontweight','b')
    text(x1,0,'I','Fontsize',16,'Fontweight','b')
    pause
    x0=x1;x1=g(x0);
    plot([x0,x0],[x0 x1])
    pause
end

clear,clc,close all
% Caso divergente, pendiente positiva
a=0;b=1;
g=@(x)-1.3*x.^2+1;
x0=0.6;
xx=linspace(a,b);
plot(xx,g(xx),'r-'), hold on
plot([a b],[a b],'k-')
axis([a,b,a,b])
set(gca,'XTick',[],'YTick',[])
hold on
title('CASO DIVERGENTE: g''(x) < - 1','Fontsize',16,'Fontweight','b')
x1=g(x0);
plot([x0 x0],[0 x1])
text(x0+0.01,0.03,['x_',num2str(0)],'Fontsize',16,'Fontweight','b')
pause
for i=1:7
    plot([x0 x1],[x1 x1])
    text(x1+0.01,0.03,['x_',num2str(i)],'Fontsize',16,'Fontweight','b')
    text(x1,0,'I','Fontsize',16,'Fontweight','b')
    pause
    x0=x1;x1=g(x0);
    plot([x0,x0],[x0 x1])
    pause
end