Here we go again with confusion caused by Nikon's naming scheme.

When I entered "AF", I meant simply "auto focus", nothing more, nothing to do with Nikon's naming scheme. I am guessing that the lens which focuses with only FX cameras is an "AF" lens - which depend on the body's having a 'AF motor', because the D3400 doesn't have one. A FX lens which focuses on all three cameras is either a "AF-S" or a "AF-P" lens, because both types have an auto focus motor in the lens. The difference in focusing is not whether the camera or lens is FX or DX, but is whether the lens is "AF" or "AF-S"/"AF-P".