Michelin Pilot super sport - proper tire pressure

Hello,

How can I estimate the correct PSI for the 17" Michelin Pilot super sport tires on my Mini Cooper S 2-door -- Both for under 100mph and over 100mph.

The side door insert shows 35PSI and in the car manual it shows 40PSI for over 100mph but it seem to be rating it for the 16" all season tires that came it -- Or is this more a function of the type of Car instead of the specific Tire?

Just checking to see if I am doing the right thing -- Currently I have all 4 at 37psi

Thanks in advance!