Using the Aitken Construction to Evaluate Pointwise Tangents to a Parabola

Starting for the Lagrange Three Point Polynomial I will develop a construction that can be used to evaluate the Slopes of the Parabola at its defining points.

The FLINE form provides a compact expression for the parametric equation for the straight line from the left-most point (XL,YL) to the right-most point (XR,YR).