Does under-eating or over-exercising slow metabolism?

2 diff responses: Overeating can actually stimulate a response from the brain that actually promotes overating. Aerobic exercise and resistance training both increase energy expenditure but this can also depend on intensity. Consuming a low calorie diet will decrease your metabolism so maintaining a nice balance of cardo and resisitance training will help in my opinion. Do not forget about proper rest and fluids.

Starvation: Yes, if you are under eating your body can go into "starvation" mode and store as much energy as possible and reduce metabolism.