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.