Applet: Gradient and directional derivative on a mountain shown as mesh plot
The dark red point can be moved along the mountain range whose height is given by $f(x,y)$. The dark blue vector points in the direction of the gradient. The magnitude of the gradient is shown by the dark blue line on the light green slider. The light green vector points at an angle $\theta$ (changeable via the top slider) from the gradient; the directional derivative in that direction is shown by the light green line on the light green slider. The dark blue and the light green vectors are shown as three-dimensional vectors titling up or down the mountain, and hence are not exactly the two dimensional vectors $\nabla f$ or the $\vc{u}$ of $D_{\vc{u}}f$.
Applet file: mountdirectgrad.m
General information about LiveGraphics3D applets
This applet was created using LiveGraphics3D. To manipulate it, you can
- click and drag to rotate in any direction,
- shift + click and drag up/down to zoom out/in,
- shift + click and drag left/right to rotate around an axis coming out of the screen, and
- press Home to reset to the original view.
Most of the LiveGraphics3D applets have parameters that you can change. In general, you can click and drag points or balls around to change the parameters.
Since these applets use Java, you must have Java installed and properly configured in your browser for the them to display. You can get Java here. If you have trouble getting them to display in your browser, you can visit the LiveGraphics3D troubleshooting page for information on how to get the Java applets to work.
On occasion, even when Java is configured correctly, the Java applets don't load the first time and one instead sees an error message. You can wait a few moments to see if the applet will eventually load itself anyway. You can also reload the page to see if the applet will properly load. Sometimes, one needs to do this multiple times.
