I have two specific sigmoid functions with domain in $[0,\infty)$ that depend on a common set of parameters. I was able to show that they have the same limit at infinity and that the dashed curve is above the back curve at $0$ (please see figure below). I now need to show that they do not intersect. I was wondering if there are any general results on the maximum number of intersections of two sigmoid curves? It seems to be $3$, but I haven't been able to obtain a proof for this. Such a result would definitely be a good start for me. Any suggestion is much appreciated.
2026-03-31 07:07:16.1774940836
What is the maximum number of intersections of two sigmoid curves?
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