Applet: Directional derivative on a mountain shown as mesh plot
The height of a mountain ranged described by a function $f(x,y)$ is shown as a mesh plot. A point $\vc{b}$ (in dark red) can be moved with the mouse. The vector $\vc{v}$ (the light green vector) points at an angle $\theta$ from east, which can be changed by dragging the red point on the top slider. Although $\vc{b}$ and $\vc{v}$ are in three dimensions, we can imagine projecting them to the $xy$-plane, giving the point $\vc{a}$ and unit vector $\vc{u}$. The value of the directional derivative $D_{\vc{u}}f(\vc{a})$ is shown by the bottom (light green) slider labeled by “Duf”.
Applet file: mountdirect.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.
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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.
