a = -1;
b = 3/2;
x = linspace(a, b, 100);
g = @(x)((3+x-2*x.^2).^(1/4));
plot(x, g(x), '-r');
hold on;

x1 = [a, b, b, a, a];
y1 = [a, a, b, b, a];
plot (x1, y1, 'Linewidth', 3)
plot(x, x, '-g');

syms arg;
dg = matlabFunction(diff(g(arg)));
figure;
hold on;
plot(x, dg(x));
plot([a, b],[1, 1]);
plot([a, b],[-1, -1]);

a = 0.8;
b = 1.27;
% x = linspace(a, b, 100);
% g = @(x)((3+x-2*x.^2).^(1/4));
% syms arg;
% dg = matlabFunction(diff(g(arg)));
% figure;
% hold on;
% plot(x, dg(x));
% plot([a, b],[1, 1]);
% plot([a, b],[-1, -1]);

figure;
hold on;
f = @(x)(x.^4 + 2*x.^2 - x - 3);
plot(x, f(x));
plot([a, b], 0)
xsol = punctFix(g, 1, 10^(-5));

plot(xsol, f(xsol), 'o', 'MarkerSize', 10);

function xsol = punctFix(g, x0, eps)

x = g(x0);
while(abs(x - x0) < eps)

   x0 = x;
   x = g(x0);

end

xsol = x;

end