15. Whenever a person coughs, the radius of the main air passages to the lungs decreases. We wish to determine at what radius the velocity ofthe expelled air will be maximum. Let v denote the function which gives the velocity of air through a particular air passage at a radius r of that passage. Under usual conditions, it has been found that the following relationship prevails: v(r) 2 cr2 [r0 r) where C is a positive constant and r0 is the radius ofthe air passage at atmosphere pressure