First constructive proof of Mean Value Theorem

The most important aspect of the mean value theorem is that it is an arithmetic mean of the ordinates of a function f, which is stated in terms of the difference of ordinates of F, where F is the primitive of f. It is completely unremarkable that a c exists in a given interval such that f'(c) = [ f(b) - f(a) ] / (b-a).

Proof using mainstream calculus and a patch (positional derivative) I created to make it possible:

https://drive.google.com/open?id=0B-mOEooW03iLZG1pNlVIX2RTR0E

Proof using the rigorous New Calculus:

https://drive.google.com/open?id=0B-mOEooW03iLblJNLWJUeGxqV0E

You won't find either of these proofs published anywhere else because if they were, this would amount to plagiarism and copyright infringement. ... https://www.youtube.com/watch?v=tlp590sHgw8