A person coughs when a foreign object is in the windpipe. The velocity of the cough depends on the size of the object. Suppose a person has a windpipe with a 26-mm

radius. If a foreign object has a radius r, in millimeters, then the velocity V, in millimeters/second, needed to remove the object by a cough is given by the following equation, where k is some positive constant. For what size object is the maximum velocity needed to remove the object?

V(r)=k(26r^2-r^3), 0< or = to r