Respuesta :
The maximum concentration is greatest at; t = 4.926 hours
How to find the time at maximum concentration?
We are given the equation that represents the concentration as;
C = (3t² + t)/(50 + t³)
The maximum value of C is obtained when the slope of C' is zero (can be a local maxima too). So we are going to find solutions of C'.
C' = (-3t⁴ - 2t³ + 300t + 50)/(50 + t³)
At C' = 0, we have;
-3t⁴ - 2t³ + 300t + 50 = 0
Using online polynomial root calculator, the only valid root of this is;
t = 4.926 hours
Thus, the maximum concentration is greatest at t = 4.926 hours
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