When you cough, your windpipe contracts. The speed,v, with which air comes out depends on the radius,r, of your windpipe. IfRis the normal (rest) radius of your windpipe, then forr≤R, the speed is given by the following formula, whereais a positive constant.v=a(R-r)r2

1. Find v'(r)

2. What value maximizes the value of r?

#2 is pretty straight forward after finding #1. Im just having trouble figuring it out.