I had recently asked the question:
Logistic function passing through two points?
which received a very helpful answer. However, I'd like to ask your help again as the formulation of the problem has slightly changed and i'm lost...
Problem:
Given two points: $(x_l, y_l)$ and $(x_u, y_u)$
with: $x_l < x_u$ and $y_l < y_u$,
and given that the higher asymptote is one ($\lim_{x\to+\infty}f(x)=1$)
what's the logistic function that passes through the two points and the origin $(0, 0)$?
Thanks!