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 r ≤ R, the speed is given by the following formula, where a is a positive constant.
v = a(R - r)r^2
(a) Find v '(r).
v '(r) =
(b) What value of r maximizes the speed?
so i believe to find the value of that r that maximizes speed, you would have to set the derivative equal to 0 and solve. However im having trouble finding the derivative, any help? thanks...