1. Start by dragging the point [i]X[/i] to the right and to the left. You should find that it stays on the function [i]f[/i]([i]t[/i]) plotted in gold. This function is sin([i]t[/i]), so [i]X[/i] is showing the value of the sine function at different times.

2. GeoGebra can determine the line that is tangent to a curve at any point. To see that tangent line for [i]X[/i], click on the circle next to "a:" in the "Line" section on the left side of the display above. Then you should be able to see what happens as you drag [i]X[/i] to the left and to the right.[br][br]3. The slope of the tangent line is taken to be the instantaneous slope of the curve, and the point "[i]V[/i]" has been set equal to that slope. To see [i]V[/i], click on the circle next to "V =" in the "Point" section on the left side of the display. You should see, as you drag [i]X[/i] back and forth, that the value of [i]V[/i] changes and that it matches the slope of the line [i]a[/i]. You may want to turn off line [i]a[/i] at this point, by clicking on the circle next to it on the left side of the display.[br][br]4. We can think of [i]V[/i] as itself tracing out some function, and in fact we can see that function by showing [i]g[/i]([i]t[/i]) by clicking on the circle next to "g(t) =" in the "Function" section on the left side of the display. What function is this? It's the cosine function! So the slope (or derivative) of sine is cosine.[br][br]5. We can repeat this process with the function [i]g[/i]([i]t[/i]). That is, we can find the slope of it at any point. We just have GeoGebra draw a tangent line to the curve where V is. This line is [i]b[/i] if you want to show it; and the value of the slope of that tangent line is the point [i]A[/i], which you can also make visible.