If f(x) is 6x/(0.02x^2 +5.2), the maximum concentration of antibiotic is about 9.303 ppm.
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When the numbers are written as rational numbers, the derivative can be found to be
.. f'(x) = 300(260 -x^2)/(260 +x^2)^2
This is zero for
.. x = ±2√65
And the value of f(x) there is
.. f(2√65) = 15√(5/13) ≈ 9.3026
