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

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

anonymous · Answer

Since this is a quadratic function that opens down (a negative quadratic term), the maximum will be at the vertex.

The vertex's x-coord will be -b/2a.

You can plug the result back into the original equation to get the max concentration.

anonymous · Answer

@ali.qamer 
  Start with t = -b/ 2a = ....?
Do you still need help?