GeoGebra, along with linking functions and curves, also provides an extensive list of tools for performing mathematics operations. This list can be accessed by clicking the icon  to the right of the Input window.

The example below uses just two of the tools, Derivative and Intersect.

In AC circuits the voltage is constantly changing. Is the rate of change in voltage constant? If it is not constant when is the rate of change at a maximum?

A question such as the above could be solved in a number of ways. One approach might be to use calculus and find the derivative function for the voltage vs time curve and look to see where this is a maximum.

Since we have the function f(x) and curve f defined, typing the command Derivative[f] in the Input window produces the required operation.

From the graph of the derivative function (in red) we can see that the maximums, both positive and negative, for rates of change occur when the AC voltage is 0. By adjusting the frequency and maximum voltage, and possibly changing the scale of the graph a student can observe that this relationship always holds.

In the case above it appears that the greatest rate of change in voltage, or the points at which the voltage is 0, are at 0, 2.5, 5.0, and 7.5 on the visible part of the x-axis. We could check to see if these are in fact the x-values we are looking for by having GeoGebra locate the points where the voltage function, f(x), has a value of 0. To do this we will introduce a second function g(x)=0 (the x-axis) and use the Intersect command.

Intersect[f,g,0,1]

The numbers 0 and 1 tell GeoGebra that we want to look for the intersection between x=0 and x=1. The results can be seen in the GeoGebra applet below.