Question

When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream after t minutes is given by
C(t) = 0.06t − 0.0002t2,
where 0 ≤ t ≤ 240 and the concentration is measured in mg/L.

When is the maximum serum concentration reached?
t =______ min

What is the maximum concentration?
________mg/L

Answer 1

sorry its 0.0002t^2

Answer 2

to find the extremum(maximum or minimum) value of a function say C(t), differentiate it with respect to dependent variable and make it equal to zero. In this example dependent variable it 't' and the equation becomes
0.06-0.0004*t=0;
which gives t = 0.06/0.0004=150 min
and to get the amount substitute t back into C(t), which gives you
C(150) = 0.06*150-0.0002*(150^2)=4.5 mg/L