format long;
es = (.5 * (10 ^ -3));
f = @(z) z ^ 3 - 4 * z + 1;
x0 = 0;
x1 = 1;
x(1) = x0;
for i = 2:1:10
    %ans0 = f(x0);
    ans0 = (x0 ^ 3) - (4 * x0) + 1;
    ans1 = (x1 ^ 3) - (4 * x1) + 1;
    x(i) = x0 - ((ans0 * (x1 - x0)) / (ans1 - ans0));
    ans2 = (x(i) ^ 3) - (4 * x(i)) + 1;
    if(ans0 > 0 && ans2 < 0) || (ans0 < 0 && ans2 > 0)
        x1 = x(i);
    end
    if(ans1 > 0 && ans2 < 0) || (ans1 < 0 && ans2 > 0)
        x0 = x(i);
    end
    ea = abs(((x(i) - x(i - 1)) * 100 )/ x(i));
    %disp(ea);
    arr(i - 1) = ea;
    fprintf('%.5f %.5f %.5f --> %.5f\n', ans0, ans1, ans2, x(i));
    if(abs(ea) < abs(es))
        break;
    end
    %plot(x);
    plot(arr);
end



--------------------------------------------------------------------------


format long;
es = .5 * (10^-1);
current = 1;
fprintf('%d %d\n', 1, 1);
for i = 1:1:100
    prev = current;
    current = current + ((.5 ^ i) / factorial(i));
    ea = ((current - prev) * 100) / current;
    fprintf('%d %f %.4f\n', i + 1, current, ea);
    %if(abs(ea) < abs(es))
    if(ea < es)
        break;
    end

end