File:Lagrange simple.jpg

Source Code
The graph was made in Matlab with the following source code % Function data [X,Y] = meshgrid(-2:0.01:2, -2:0.01:2); Z = (X.^2).*Y;

% Constraint data t = -pi:0.01:pi; xc = sqrt(3)*cos(t); yc = sqrt(3)*sin(t); zc = xc.^2 .* yc;

% Plot graph and constraint figure; meshc(X,Y,Z); hold on; plot3(xc, yc, zc, 'k', 'LineWidth', 2); plot3(xc, yc ,-10*ones(1,length(t)), 'k', 'LineWidth', 1); set(gcf, 'Color', [1 1 1]); set(gcf, 'Position', [46 107 767 682]); % Axis labels text(0.2, -3, -10, 'x'); text(2.5, -.5, -10, 'y'); text(-2.4, -2, 0, 'z');

% Annotations of the max and min points % Point indicating max #1 plot3(sqrt(2), 1, 2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(sqrt(2), 1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',...	'String', '$$(\sqrt{2}, 1, 2)$$',...	'Position', [1.1 .1 2.1],...	'FontSize', 20); % Point indicating max #2 plot3(-sqrt(2), 1, 2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(-sqrt(2), 1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',...	'String', '$$(-\sqrt{2}, 1, 2)$$',...	'Position', [-1.6 .1 2.1],...	'FontSize', 20); % Point indicating min #1 plot3(sqrt(2), -1, -2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(sqrt(2), -1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); plot3(0,1,-3,'kx') text('Interpreter', 'latex',...	'String', '$$(\sqrt{2}, -1, -2)$$',...	'Position', [.5 -.8 -1.4],...	'FontSize', 20); % Point indicating min #2 plot3(-sqrt(2), -1, -2, 'kx', 'MarkerSize', 14, 'LineWidth', 2); plot3(-sqrt(2), -1, -10, 'kx', 'MarkerSize', 10, 'LineWidth', 2); text('Interpreter', 'latex',...	'String', '$$(-\sqrt{2}, -1, -2)$$',...	'Position', [-1.9 -.8 -1],...	'FontSize', 20); hold off; view([25 18]);