Here we explore the first derivative of polynomial functions up to order 4. The general function considered is. The function is initially created with and the other constants equal to zero, that is a parabola.
The point A is a point on the curve and the point D represents the value of the derivative at the point A. The black line is the tangent to the curve at the point A. With your mouse you can move the point A along the curve and notice also that the tangent changes slope. At the same time, the point D moves and its motion is traced, in other words, D traces out the derivative of , that is .
There are several things you can do here:
1. Change the value of and see how this changes the derivative.
2. Change the value of and see what effect this has on the derivative.
3. Increase the order of the polynomial by change the values of and .
To remove an unwanted trace, simple adjust the zoom on the screen. The reset button at the top right will reset the initial parabola example.