Question

For some positive constant C, a patient's temperature change T, due to a dose, D, of a drug is given by T= (C/2 - D/3)D^2. What dosage maximizes the temperature change? The sensitivity of the body to the drug is defined as dT/dD. What dosage maximizes sensitivity?
For some positive constant C, a patient's temperature change T, due to a dose, D, of a drug is given by T= (C/2 - D/3)D^2. What dosage maximizes the temperature change? The sensitivity of the body to the drug is defined as dT/dD. What dosage maximizes sensitivity?
@Mathematics

Answer 1

to maximize T , set dT/dD = 0
to maximize sensitivity, set dT^2/dD = 0 **2nd derivative**

dT/dD = CD -D^2
dT^2/dD = C -2D

CD -D^2 = 0
D(C-D) = 0
Assume D>0
C-D = 0
D=C
--> when dosage equals C, T is maximized

C -2D = 0
D = C/2
--> when dosage equals C/2, sensitivity is maximized