
Re: 1.39  What exactly is the Mean value Theorem?
Posted:
Jun 19, 2014 7:10 AM


John Gabriel <thenewcalculus@gmail.com> wrote in news:929be574b8814442ad67e741fb1823de@googlegroups.com:
> In mainstream mythmatics, the MVT is ignorantly defined as follows: > > If f is a differentiable function on (a,b), then there is at least one > point c, such that a secant line with endpoints (a,f(a)) and (b,f(b)) > is parallel to the tangent line at c.
That is correct. > But the converse of this is NOT true in mainstream calculus: > > If f is a differentiable function on (a,b), and a tangent line exists > at c, then a parallel secant line exists with endpoints (a,f(a)) and > (b,f(b)).
Because that is NOT correct, and easily shown to be false.
There is no requirements the converse need to be true. > However, the MVT works regardless of the converse being true.
A) What do you mean by 'works' B) Why do you think whether or not a converse is true should be relevant?
> The > reason for this, is that ignorant baboons (that would be you) do not > know its real meaning. In the New Calculus, the MVT is defined > properly: > > If f is a differentiable function over (a,b), then {f(b)f(a)}/(ba) > is the (natural) average of all the ordinates of f' over (a,b).
OMG ... no. Really? That is simply hilarious. You're a total fucking moron.

