High or Low Points on a Curve

Why: Sight distance, clearance, cover pipes, and investigate drainage.
At the highest or lowest point, the tangent is horizontal, the derivative of Y w.r.t X = 0
Deriving the general formula gives: X = g1 L/(g1 - g2) = -g1/r where: X is the distance in sta from BVC to the high or low point.
Substitute in the tangent offset equation to get the elevation of that point.