The concentration of a drug t hours after being injected is given by

C (t) = (0.3t) / (t^2+5). Find the time when the concentration is at a maximum. Give your answer accurate to at least 2 decimal places.

t = 2.236 hours

or 2 hours 14.16 minutes.

Step-by-step explanation:

C = (0.3t) / (t^2 + 5) where C is the concentration of the drug.

Finding the derivative using the Quotient rule:

C' = (t^2 + 5) (0.3) - (0.3t) * 2t / (t^2 + 5) ^2

C' = 0.3t^2 + 1.5 - 0.6t^2 / (t^2 + 5) ^2

C' = - 0.3t^2 + 1.5 / (t^2 + 5) ^2

C is at a maximum when the derivative is zero.

Equating this to zero:

-0.3t^2 + 1.5 / (t^2 + 5) ^2 = 0

-0.3t^2 + 1.5 = 0

-0.3t^2 = - 1.5

t^2 = - 1.5 / - 0.3 = 5

t = √5

t = 2.236 hours.