Brain Teaser - Minimum distance between two curves

[Vtile]

."Piece of cake" with Sensored. I have theary with arithmetics, but francly I have more important things to do atm. than reviving this particular thing to my head. Coffee break is over.

Edit, Sensored

Edit2. If I'm not terribly mistaken the points are: x=0.34368 and x=0.39685 .. But I might just be totally wrong, the still in learning with 50g doesn't make it any easier. OK Couldn't resist, back to work.
Edit3. Yep, it is wrong, would have been too easy.