Polynomials and Multiple Derivatives


In this applet you can move the seven red control points up and down. A 6th degree polynomial is fitted to these points, so you change the polynomial by moving the control points.


  1. If you take the derivative of a 6th degree polynomial, must it always be the case that you get a 5th degree polynomial? Are there any exceptions?
  2. Looking at the graph of a polynomial, how can you tell, in general, what the degree of the polynomial is?
  3. When the slider shows `d = 0`, the original 6th degree polynomial is displayed. Higher values of `d` take higher derivatives. Play with the slider and confirm that the derivatives of the polynomial behave the way you expect.