Suppose that body temperature 1 hour afer receiving x mg of drug is given by
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
In order to maximize sensitivity, we're interested to see when its derivative is equal to 0. You're given that the sensitivty of the body to the drug dosage is given by T(x)=102-1/6 x^2(1-x/9), which is:
Originally Posted by gracy
T'(x) = (x^2/18) - (x/3); you are told that it is between 0 and 6, which is obtained by setting this derivative equal to zero.
Now, in order to maximize it, we need to find the derivative of T'(x) and set it equal to 0.
T''(x) = (x/9) - (1/3) = (x-3)/9
0 = (x-3)/9
x = 3
Thus, 3 mg will maximize sensitivity.