Question: When you cough, your windpipe contracts. The speed, v(r), with which you expel air depends on the radius, r, of your windpipe. If a is the normal (rest) radius of your windpipe, then for 0 ≤ r ≤ a, the speed is given by: v(r) = k(a - r)r2 where k is a positive constant. What value of r maximizes the speed? For what value is the speed minimized?