Given a third degree polynomial curve, such as the GREEN curve below,
and a cutt-off point, indicated by the ORANGE line below, where the cutt-of point is placed on or near the cusp/inflection point of the GREEN line... like so:
How do I produce a left-most line segment that acts as a continuation of the green line?
I am looking for something like so, where the curve equation segment I am seeking is within the blue box:
And the x value for first inflection point is known.
The equation for the original GREEN line can be something like so (example only)
$$-3.5*10^-6 x^3 - 0.0066 x^2 + 1.3 x - 30$$
I am looking for methods, techniques, suggestions, actual steps to take for this class of problem... to replace the part of the curve with a new curve, of similar slope.. and I am seeking the equation for the segment of the new curve.