File:Lagrange simple.jpg

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Source Code[edit]

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]);

Licensing[edit]

I, the copyright holder of this work, hereby grant the permission to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. GFDL GNU Free Documentation License //en.wikipedia.org/wiki/Wikipedia:Text_of_the_GNU_Free_Documentation_License

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. This licensing tag was added to this file as part of the GFDL licensing update. Cc-by-sa-3.0Attribution-ShareAlike 3.0https://creativecommons.org/licenses/by-sa/3.0/

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