### Applet: Partial derivatives of heating cost

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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 red line, and the partial derivative $\displaystyle \pdiff{h}{I}$ corresponds to the slope of the green line. You can drag the blue point around to change the values of $T$ and $I$ where the partial derivatives are calculated.

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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.