Suppose that the body temperature 30 minutes after receiving x mg of a drug is given by for . The absolute value of the derivative, , is defined as the sensitivity of the body to the drug dosage. Find the dosage that maximizes sensitivity.
A) x = 4 mg
B) x = 6 mg
C) x = 2 mg
D) x = 3 mg

Question

Suppose that the body temperature 30 minutes after receiving x mg of a drug is given by  for  . The absolute value of the derivative,  , is defined as the sensitivity of the body to the drug dosage. Find the dosage that maximizes sensitivity.
A) x = 4 mg 
B) x = 6 mg 
C) x = 2 mg 
D) x = 3 mg

Quizplus · Accepted Answer

To find the dosage that maximizes sensitivity, we need to find when the derivative is at its maximum. Taking the derivative of the given function, we get:
11eaa88b_9240_af8d_a696_6b2a6f1c120a_TB5869_11

Now, setting the derivative equal to 0 and solving for x:
11eaa88b_9240_9d39_a696_adf48355ccf1_TB5869_11
11eaa88b_9240_4f11_a696_e1c3046e0717_TB5869_11

So, the dosage that maximizes sensitivity is x = 2 mg. Therefore, the answer is C).

Suppose That the Body Temperature 30 Minutes After Receiving X