clear, clc, close all
f=@(x)x.^3-2*x.^2+1;

a=0;b=-1;N=4;
xx=linspace(a,b);
fa=f(a); fb=f(b);  
x=b-f(b)*(b-a)/(f(b)-f(a)); fx=f(x);

for n=1:N
    figure(1)
    clf
    hold on
    plot(xx,f(xx))
    plot([-1 0],[0,0],'k-')
    set(gca,'XTick',[],'YTick',[])
    box on
    title('Secante','Fontsize',16,'Fontweight','b')
    if f(a)*f(b)<0
    plot([a b],[f(a) f(b)],'r-','linewidth',2)
    else
         if abs(f(a))>abs(f(b))
             plot([a b-f(b)*(b-a)/(f(b)-f(a))],[f(a) 0],'r-','linewidth',2)
         else
             plot([b b-f(b)*(b-a)/(f(b)-f(a))],[f(b) 0],'r-','linewidth',2)
         end  
    end
    plot([a a],[0 f(a)],'b-','linewidth',2)
    text(a+0.01,0.1,['x_',num2str(n-1)],'Fontsize',16,'Fontweight','b')
    plot([b b],[0 f(b)],'b-','linewidth',2)
    text(b+0.01,0.1,['x_',num2str(n)],'Fontsize',16,'Fontweight','b')
    pause
    x=b-f(b)*(b-a)/(f(b)-f(a)); fx=f(x);
    plot([x x],[0 f(x)],'b-','linewidth',2)
    text(x+0.01,0.1,['x_',num2str(n+1)],'Fontsize',16,'Fontweight','b')
    pause
    a=b;b=x;
end