yesterday my lane departure warning light came on in the morning, and went off and on a few times and finally went off.

Today it came on again.  

Any ideas about its cause?

2015 Crosstrek XV, CVT 6000 miles--I don't drive a lot

 

Also, when I accelerate the RPMs exceed 3000 rpm even when I nudge it.  I don 't like that.

With my old subaru I kept it under 3000 almost all of the time.

Does the light come on when you just get into the car or on the road or when stopped?

Around 4000 is the best place in the power curve.  Not going that high, is just putting more strain on the engine and you are starting up slowly.  If you like keeping it under 3000, stay in the slow lane or get out of my way.