When medicine is administered, reaction (measured in change of blood pressure or temperature) can be modeled by
R = m2 (c/2 - m/3)
where c is a positive constant and m is the amount of medicine absorbed into the blood. The sensitivity to the medication is defined to be the rate of change of reaction R with respect to the amount of medicine m absorbed in the blood.
(a) Find the sensitivity.
(b) Find the instantaneous rate of change of sensitivity with respect to the amount of medicine absorbed in the blood.
(c) Which order derivative of reaction gives the rate of change of sensitivity?