In this demonstration, the "Function Graph: f(x,y)" window shows the graph of f color coded by the sign of the partials derivatives.

Purple represents f_x > 0 and f_y > 0.
Red represents f_x > 0 but f_y < 0.
Blue represents f_y > 0 but f_x < 0.
White repsesents f_x < 0 and f_y < 0.

In the window, "f_x(x,y) > 0", just that part of the surface where the x-derivative is greater than zero is colored (in red). The window "f_y(x,y) > 0" allows you to view just the region of the surface where f_y is greater than zero (in blue).

The rotations of these two windows are linked with the main window, so even rotating the surface around you will see how the colored regions from the main window are obtained by just "adding up" the colorations of the minor windows. I.e. the coloring is purple if and only if both f_x(x,y) and f_y(x,y) are greater than zero.

The "Fold Sets" window shows the fold set in the x-direction in red, and the fold set in the y-direction in blue. Their intersections are critical points of the graph.