The velocity, v, with which air comes out depends on the radius, r, of your windpipe.

The velocity, 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 velocity is given by v = a(R - r)r2 , where a is a positive constant. What value of r maximizes the velocity? 4. The temperature change, T , in a patient generated by a dose, D of a particular drug is given by T = where C is a positive constant. (a) What dose maximizes the temperature change? DT (b) The sensitivity of the body, at dosage D, to the drug is defined to be . What dosage maximizes dD sensitivity?