How to tire pressure affect a car's performance?

Question

a) will higher or lower pressure improve speed
b) will higher or lower pressure improve handling and cornering
c) overall for optimal speed and cornering which is better
-even(same) pressure in front and rear tires,
-lower pressure in front and higer pressure in rear tires
-higher pressure in front and lower pressure in rear tires

Answer 1

The folks who design tires label them with the optimal recommended tire pressure for a reason. A tire that's under inflated is a serious road hazzard. Driving on tires that are under inflated, is like driving on wet ice while you're drunk. your car will forever try and go in directions other than the course you are steering. They also create excess drag and friction with the road and therefor are bad for gas milage.
A tire that is over inflated, while not nearly as unmanagable allows for a minimal amount of rubber on the road. And with too little friction, the tire won't have nearly the amount of traction, allowing you to steer in the direction you intend to go.

Answer 2

Higher pressure up to tires limit will improve speed, but will reduce adhesion to pavement on high speed turns. So actual pressure used is a compromise. Usually more pressure is needed on the front as more weight is on the front due to the engine. Just need to vary mfg. recommendation unit you get what you want, but do not exceed tires recommended limits as embossed on the tire sidewall. also grade of tire is a factor