Originally Posted by

**AfterShock** 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:

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.