Originally Posted by

**Dave J** The question is.

The speed of air escaping through your trachea when you cough is a function of the force due to chest contraction and the size of the trachea. It can be modelled by the equation

S = F(1+0.9r^2-r^3) where F is the constant force of youre chest contraction, r is the radius of your trachiea in centimeters, S is the speed of the airflow.

Determine the max speed of airflow.

I know to find the max speed I need to take the derivative and find critical numbers, but how do I do that when there is the F and the r??