When we cough, the trachea contracts to increase the velocity of the air going out. this raises the question of how much it should contract to maximize the velocity and whether it really contracts that much when we cough. under reasonable assumptions about the elasticity of the tracheal wall, and about how the air near the wall is slowed by friction, the average flow velocity "v" can be modeled by the equation " V= c(r0 - r) r^2 cm/sec for r0/2 is less than or equal to r which is less than or equal to r0 where r0 is the rest radius of the trachea in cm, and c is a positive constant. find the value of r which maximizes v.