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there is not info to be able to give a definite answer
to work it out
you have top know the diff ratio, wheel tyre circumference to be able to work from rpms of the engine to road speed
However as a pointer, most cars will be around 3200 rpms at 60mph as this will be direct drive and od causes a drop in rpms
Being an automatic find yourself a good section of low traffic road and start from stop slowly increase the rpms and watch the rpms. keeping the accelerator steady you will see when the auto changes by a drop in rpms. slowly increase road sped until you see the next drop in rpms and so on. Over drive normally comes in around 55 mph or around 3000rpms
I would think that it is working because 3500rpms at 75mph is reasonable rpms to be expected. If it wasn't working I would expect the rpms to be around 3800 to 4000.at 75mph
Cars are design to run at a higher idle at start up to warm them up quick. There is a sensor that reads water temperature and tells your car's computer how fast to idle. Your RPMs seem slightly high but not out of the norm. Does idle ever drop to around 600/800 after about a minute? If not, your engine temperature sensor maybe defective.