To increase the velocity of the air flowing through the trachea when a human coughs, the body contracts the windpipe, producing a more effective cough. Tuchinsky formulated that the velocity of air that is flowing through the trachea during a cough is

V = C(R0 - R)R²,

where C is a constant based on individual body characteristics, R₀ is the radius of the windpipe before the cough, and R is the radius of the windpipe during the cough. It can be shown that the maximum velocity of the cough occurs when dV/dR = 0. Find the value of R that maximizes the velocity.