Applet: Partial derivatives of heating cost
The partial derivatives of the heating cost $h(T,I)$ with respect to outside temperature $T$ and amount of insulation $I$ can be viewed as the slopes of the graph in the $T$ direction and in the $I$ direction. The partial derivative $\displaystyle \pdiff{h}{T}$ corresponds to the slope of the dark blue line, and the partial derivative $\displaystyle \pdiff{h}{I}$ corresponds to the slope of the light green line. (The numerical values are labeled as $dh/dT$ and $dh/dI$ because we couldn't get a $\partial$ character to display in the graph.) You can drag the red point around to change the values of $T$ and $I$ where the partial derivatives are calculated.
Applet file: pderivheatex.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.
