Biomedical: Coughing When you cough, you are using a high-speed stream of air to clear y...

Biomedical: Coughing When you cough, you are using a high-speed stream of air to clear your trachea (windpipe). During a cough your trachea contracts, forcing the air to move faster, but also increasing the friction. If a trachea contracts from a normal (rest) radius of 3 centimeters to a radius of r centimeters, the velocity of the airstream is , where c is a positive constant depending on the length and the elasticity of the trachea. Find the radius r that maximizes this velocity. (X-ray pictures verify that the trachea does indeed contract to this radius.)