Question

The temperature change, T, in a patient generated by a dose, D, of a drug is given by
T=(C/2-D/3)D^2

where C is a postitive constant

what dosage maximizes the temperature change?

the sensitivity of the body, at dosage D, to the drug is defined as dT/dD what dosage maximizes sensitivity.

Answer 1

the function is

\[T(D)=\frac{\frac{C}{2}-\frac{D}{3}}{D^2}\]

Answer 2

C is a constant in this yes? do take derivative wrt D , set = 0 and solve for D

Answer 3

\[T=(\frac{C}{2}-\frac{D}{3})D^2\]

Answer 4

oh wait not what you wrote. is it
\[T(D)=(\frac{C}{2}-\frac{D}{3})D^2\]?

Answer 5

got it. multiply out to get
\[\frac{CD^2}{2}-\frac{D^3}{3}\]

Answer 6

take the derivative wrt D to get
\[T'(D)=CD-D^2\]

Answer 7

okay...

Answer 8

set = 0 and solve for D via
\[CD-D^2=0\]
\[D(C-D)=0\]
\[D=0\] (unlikely) or
\[D=C\] which is your answer.

Answer 9

i have both

Answer 10

well it is certainly unlikely that D = 0 is an answer since if D = 0 you get T(D) = 0

Answer 11

there are no values in the question so i would say D=C

Answer 12

so what's that? for the dosage that maximizes the temperature change if so how do you find part II