Visualization of graphs with Functions of Two Variables

Later we will have other explorations with this applet.

For now, make sure the applet is in input mode (you can get there by using the Show menu). Look at the plots for the various function choices. Use the mouse to move the plot around in three dimensions.

You can also enter functions by hand.
Try the function z = 2*sqrt(x^2 + y^2).

Use the Show menu to put the applet into Partial Derivatives mode and put the pink dot (in the graph at the lower right) at (0,0). This mode shows many things. What we're interested in at the moment is the slices on the 3D plot. These are the traces of the graph in the xz and yz planes. If you move the pink dot you get the traces in planes parallel to the xz and yz planes, and the slopes of the corresponding tangent lines to those trace curves.