The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by interval where N is decreasing. When is the concentration of the drug increasing and when is it decreasing?
A) Decreasing on (0, 2.5)
B) Increasing on (0, 1) and decreasing on (1, 5)
C) Increasing on (0, 10)
D) The concentration of the drug is constant.

Question

The concentration (in milligrams/cubic centimeter) of a certain drug in a patient's body t hr after injection is given by  interval where N is decreasing. When is the concentration of the drug increasing and when is it decreasing?
A) Decreasing on (0, 2.5) 
B) Increasing on (0, 1) and decreasing on (1, 5) 
C) Increasing on (0, 10) 
D) The concentration of the drug is constant.

Quizplus · Accepted Answer

Taking the derivative of the function with respect to t, we get f'(t) = -0.08t^2 + 2.4t - 11 Setting f'(t) = 0 and solving for t, we get t = 1.5 or t = 15 This gives us two critical points. We can then check the sign of f'(t) in each interval to determine whether the concentration of the drug is increasing or decreasing. For t < 1.5, we have f'(t) < 0, so the concentration of the drug is decreasing. For 1.5 < t < 5, we have f'(t) > 0, so the concentration of the drug is increasing. For t > 5, we have f'(t) < 0, so the concentration of the drug is decreasing. Therefore, the concentration of the drug is increasing on the interval (0, 1) and decreasing on the interval (1, 5). Option B is the correct answer.

The Concentration (In Milligrams/cubic Centimeter) of a Certain Drug in a Patient's