The last few activities have shown us that Geogebra is able to calculate derivatives. The functions [code]f[/code] and [code]g[/code] and their derivatives (as calculated by Geogebra in the previous activities) are displayed below.[br][br]Just to show you this isn't a fluke however, try entering your own function. If you can't think of one, maybe try [br][code][br]george(x)=-5x^2+12x-2[br][/code] [br]Then, after you've done so, type [code]derivative(functionname)[/code] but of course replace [code]functionname[/code] with your function's actual name. So, if you used my suggestion, you should type [br][code][br]derivative(george)[/code]

If you really stop to think, this is kind of amazing. How is Geogebra doing this? Is it somehow taking a look at the slopes of the tangent lines really quickly, and then making a statistical model? Or is it doing something even cleverer? [br][br]It turns out it's doing something even clever...[br][br]Move forward to find out!