Notes of the original author (**Ruth Dover**):

*Drag the points to change the graph of the polynomial function and watch the derivative change accordingly. Nice choices will let the graph of the derivative stay within the given window.*

*Understanding*

*Understanding*Ask yourself:

*when the derivative is positive the function is…**when the function is decreasing the derivative is…**when the derivative crosses the x axes the function has…**when the function crosses the x axes the derivative is…**when the function has a local maximum (or minimum) the derivative…*

*Notes*

*Notes*

In this demonstration the function is a *polynomial function* passing through five movable points. You probably know that you need **3** points to find the equation of a parabola (**2**^{nd} grade polynomial with the form ) passing through them. In the same way you need **5** points to find the equation of a **quartic function** (**4**^{th} grade polynomial).

This function will have the form: and the five parameters can be found by imposing the passage of the polynomial function through the five movable points (system of 5 linear equations in 5 unknowns).

So the polynomial function represented by the blue line in the graphic window is a *quartic function* and its derivative (black line) is a cubic parabola.