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Solution: To maximize $ C(t) = \frac{3t}{t^2 + 4} $, we take its derivative using the quotient rule:
C'(t) = \frac{(3)(t^2 + 4) - 3t(2t)}{(t^2 + 4)^2} = \frac{3t^2 + 12 - 6t^2}{(t^2 + 4)^2} = \frac{-3t^2 + 12}{(t^2 + 4)^2}.
Set $ C'(t) = 0 $:

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