# need help optimization

• Dec 9th 2006, 03:15 AM
bobby77
need help optimization
Suppose that body temperature 1 hour afer receiving x mg of drug is given by
T(x)=102-(1/6) x^2(1-x/9)
for 0<=x<=6.The absolute value of the derivative,|T'(x)| is defined as sensitivty of the body to the drug dosage.Find the dosage that maximize sensitivity
• Dec 9th 2006, 09:06 AM
CaptainBlack
Quote:

Originally Posted by bobby77
Suppose that body temperature 1 hour afer receiving x mg of drug is given by
T(x)=102-(1/6) x^2(1-x/9)
for 0<=x<=6.The absolute value of the derivative,|T'(x)| is defined as sensitivty of the body to the drug dosage.Find the dosage that maximize sensitivity

Sketch y=T(x), you will find that it gas a maximum at x=0, and a minimum at x=6,
and its derivative is negative on (0,6). So |T'(x)|=-T'(x) on the interval.

So now you are looking for the maximum of -T'(x). So differentiate it and set
that derivative to zero solve for x, and substitute back into -T'(x) to find the
maximum. So you need to find the solutions of:

T''(x)=0.

RonL