calculus- biomed question

[aussieboy]

I am having trouble with this question. My main problem is i dont know what they are asking.

Suppose a drug is administered that lowers a patient’s temperature. The amount T
(in appropriate units) that the temperature is decreased is modelled by the function
T = f(D) =(C/2 - D/3) D^2
where D is greater than or = 0 is the quantity of the dose of the drug (in appropriate units).

I know you dont like list of questions but these are the only three i am having trouble with.

(a) Find the dosage D that this model predicts maximises the drop in temperature.
(b) The sensitivity to the drug of the body, at dosage D, is defined to be dT/dD.
Find the dosage D that maximises sensitivity.
(c) If a dosage D  greater than or = 0 causes an increase in temperature of the patient, then it is
called an overdose. Find the values of D that cause an overdose.

question a and b i simply dont understand what they are asking.
the graph never reaches a positive integer. I tried graphing it in excel, all the way to 1000 and still the T remained negative as D increased.

thank you very much for your help.
It is much appreciated
Sam

 

[galactus]

I am having trouble with this question. My main problem is i dont know what they are asking.

Suppose a drug is administered that lowers a patient’s temperature. The amount T
(in appropriate units) that the temperature is decreased is modelled by the function
T = f(D) =(C/2 - D/3) D^2
where D is greater than or = 0 is the quantity of the dose of the drug (in appropriate units).

I know you dont like list of questions but these are the only three i am having trouble with.

(a) Find the dosage D that this model predicts maximises the drop in temperature.

Maximization would indicate differentiation. Find the derivative of T w.r.t D, set to 0 and solve for D. C is a constant, so your solution will be in terms of C.

(b) The sensitivity to the drug of the body, at dosage D, is defined to be dT/dD.
Find the dosage D that maximises sensitivity.

Since sensitivity is dT/dD, find the second derivative of T, set to 0 and solve for D. Your solution will be in terms of C.

(c) If a dosage D  greater than or = 0 causes an increase in temperature of the patient, then it is
called an overdose. Find the values of D that cause an overdose.

\(\displaystyle \left(\frac{C}{2}-\frac{D}{3}\right)D^{2}\geq 0\). Solve the inequality for D.

question a and b i simply dont understand what they are asking.
the graph never reaches a positive integer. I tried graphing it in excel, all the way to 1000 and still the T remained negative as D increased.

thank you very much for your help.
It is much appreciated
Sam[/quote]

 

[aussieboy]

Thank you. Much appreciated. And very helpful.