Polynomial Root-Dragging

Matt Boelkins

Below we begin with a degree 6 polynomial with 6 distinct real zeros.  To see the effects of polynomial root-dragging, click and drag on any of the moveable red points and watch the function change.  What appears to happen to the relative maxima and minima during this process?  To the critical numbers?
 
 

Anderson's Polynomial Root Dragging Theorem states (essentially) that if we take any polynomial with all real, distinct zeros, and move some subset of them to the right, then all critical numbers of the function move to the right as well.