A patient's temperature change, T, due to a dose, D, of a drug is given by the following equation. C is a positive constant.
T = [(C/2)-(D/3)]D^2
(a) What dosage maximizes the temperature change?
(b) If the sensitivity of the body to the drug is defined by dT/dD, what dosage maximizes sensitivity?
Show the steps if you can. Thank you.
Optimization
2010-03-30 10:29 am
回答 (1)
2010-03-30 4:56 pm
✔ 最佳答案
(a)T = [(C/2)-(D/3)]D^2=(C/2)D^2-(1/3)D^3dT/dD=CD-D^2
when dT/dD=0
D=0 or C
when D<0, dT/dD<0
when 0<D<C, dT/dD>0
when D>C,dT/dD<0
So, T is greatest when D=C
(b)
dT/dD=CD-D^2
d^2T/dD^2=C-2D
when d^2T/dD^2 =0, D=C/2
when D<C/2, d^2T/dD^2>0
when D>C/2,d^2T/dD^2<0
So,dT/dD is greatest when D=C/2
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