## Optimization Problems

When you cough, your windpipe contracts. The speed, v, with which air comes out depends on the radius, r, of your windpipe. If R is the normal (rest) radius of your windpipe, then for rR, the speed is given by the following formula, where a is 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.