Math Insight

Applet: Level curves of an elliptic paraboloid shown with graph

The graph of the function $f(x,y)=-x^2-2y^2$ is shown is the first panel along with a level curve plot in the second panel. The level curve $f(x,y)=c$ is shown in red in the level curve plot, which is the same as the slice of the graph $z=f(x,y)$ by the plane $z=c$. You can change $c$ by dragging the plane slicing the graph up or down with the mouse. You can also change $c$ by dragging the red level curve.

Applet links

This applet is found in the pages

• Level sets

List of all applets

General information about three.js applets

The applet was made using three.js and requires Javascript as well as a browser that supports WebGL. For most three.js applets, you can drag with the mouse to rotate the view, drag with the right button to pan, and zoom in/out with the mouse wheel. Many applets contain points that you can drag to change values of variables.