[i][i]This Applet can be used to Visualizing Functions of Two Variables onto its xy-projection . [u]Here are explored[/u]:[br][/i][/i][i][i]-[b][u]E[/u][/b][/i][/i][b][i][i][u]xtrema lines[/u]. [/i][/i][/b][i][i]Points of intersection of these lines are critical points.[br][/i][/i][i]-[/i][i][i][b][u]Two methods of drawing contour lines:[/u][/b][br][/i][/i][b][color=#ff7700]Implicit method[/color][color=#1155cc]. [/color][/b][i]In this case colours of painting are dependent on the heights with respect to the x-y Plane. Lines of the same color are contour lines -similar to the [/i][i][i][color=#1e84cc]lines [/color][/i][/i][i][i]of [/i][/i][i][i][color=#0000ff]equal thickness [/color][/i][/i][i]in [color=#0000ff]Optical Interference[/color]. You can use the "Frequency" parameter to adjust the distance between the lines. [/i][i][i]Increasing the frequency, you can examine in more details the functions region with small changes of coordinates z. [br][/i][/i][b][color=#ff7700]E[/color][/b][b][color=#ff7700]xplicit method[/color][color=#1155cc]. [/color][/b][i]In this case contour lines are drawn directly on a x-y Plane. [/i][i]Both methods can be used for all points in x-y Plane and for a small area near the selected point.[br][/i][i][i]-[b][u]Critical points[/u][/b] of the function y=f(x,y) and its projection onto the x-y plane.[br][i][i]Attention: You can download the applet to your computer and Java applet will run faster.[/i][/i][/i][/i]