figure(1);

set(gcf, 'PaperUnits', 'centimeters');
xSize = 20; ySize = 15;
xLeft = (21 - xSize)/2; yTop = (30 - ySize)/2;
set(gcf,'PaperPosition', [xLeft yTop xSize ySize]);
set(gcf,'Position',[0 0 xSize*50 ySize*50]);

[X, Y] = meshgrid(-1.3:0.1:1.3, -1.3:0.1:1.3);

f = @(X, Y) X.^2 - 2*Y.^2 + X.*Y;

hold on;
t = title('Funktion $f(x_{1}, x_{2}) = x_{1}^{2} - 2x_{2}^{2} + x_{1} x_{2}$', 'interpreter', 'latex');
set(t, 'FontSize', 16);
Z = f(X, Y);
mesh(X, Y, Z);

phi = linspace(0, 2*pi, 200);
X = cos(phi);
Y = sin(phi);
Z = f(X, Y);
plot3(X, Y, Z + 0.03, 'LineWidth', 2, 'Color', 'blue');

a = [sqrt(0.5 + sqrt(9/40)) sqrt(0.5 - sqrt(9/40))];
b = [-sqrt(0.5 - sqrt(9/40)) sqrt(0.5 + sqrt(9/40))];
c = [-sqrt(0.5 + sqrt(9/40)) -sqrt(0.5 - sqrt(9/40))];
d = [sqrt(0.5 - sqrt(9/40)) -sqrt(0.5 + sqrt(9/40))];

plot3(a(1), a(2), f(a(1), a(2)), 'r.', 'MarkerSize', 25);
plot3(b(1), b(2), f(b(1), b(2)), 'r.', 'MarkerSize', 25);
plot3(c(1), c(2), f(c(1), c(2)), 'r.', 'MarkerSize', 25);
plot3(d(1), d(2), f(d(1), d(2)), 'r.', 'MarkerSize', 25);

t = text(a(1), a(2), f(a(1), a(2)) + 0.03, '$\left(\sqrt{\frac{1}{2} + \sqrt{\frac{9}{40}}}, \sqrt{\frac{1}{2} - \sqrt{\frac{9}{40}}}\right)$', 'interpreter', 'latex', 'color', 'black');
set(t, 'FontSize', 14);
t = text(b(1), b(2), f(b(1), b(2)) + 0.03, '$\left(-\sqrt{\frac{1}{2} - \sqrt{\frac{9}{40}}}, \sqrt{\frac{1}{2} + \sqrt{\frac{9}{40}}}\right)$', 'interpreter', 'latex', 'color', 'black');
set(t, 'FontSize', 14);
t = text(c(1), c(2), f(c(1), c(2)) + 0.03, '$\left(-\sqrt{\frac{1}{2} + \sqrt{\frac{9}{40}}}, -\sqrt{\frac{1}{2} - \sqrt{\frac{9}{40}}}\right)$', 'interpreter', 'latex', 'color', 'black');
set(t, 'FontSize', 14);
t = text(d(1), d(2), f(d(1), d(2)) + 0.03, '$\left(\sqrt{\frac{1}{2} - \sqrt{\frac{9}{40}}}, -\sqrt{\frac{1}{2} + \sqrt{\frac{9}{40}}}\right)$', 'interpreter', 'latex', 'color', 'black');
set(t, 'FontSize', 14);

view([147, 68]);

xlabel('x_{1}');
ylabel('x_{2}');
zlabel('f(x_{1}, x_{2})');