As the pieces below are rather old, I recently summarized my thinking on the matter in the following which is also available from Research Gate.

In The AMATYC Review, Volume 11, Number 1 (Part 2) - Fall 1989.

Editor's Note: This article extends the mathematical ideas presented by the authors in their article Integrated Precalculus and Differential Calculus: A Lagrangian Approach that appeared in the Fall, 1989 (Part 2) issue of this journal.

In The AMATYC Review, Volume 11, Number 2 - Spring 1990.

Presented at the What is happening with calculus revision session of the Joint AMS/MAA Phoenix Meeting, January 1989.

Adapted from the Lecture Notes of a Minicourse given at the Joint Mathematics Meetings in Louisville, Janauary 1990.