My impression has been, and trying to keep it simple in answer to Centaurus's question, is this:
F.D. minimum speed on SE departure is V2.
maximum V2 + 15
Speed IN = Speed Out. By that I mean if the engine failure occurs between
V2 - V2+15 the F.D. will hold that speed.
If you rotate late/slow and speed is high F.D. will command a pitch up then stabalise at V2 +15. If you rotate too fast/high then F.D will command an attitude to give a minimum V/S to accelerate to V2 and then pitch up to maintain.
Stand correction if not quite so.
Another question:
Does anyone know why on NG's Boeing have altered the white bug to set at
V2 +15 for departure and Vref +20 for approach? This softwear change appeared with no explanation and no-one in our outfit knows why.