The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function below, where I is the light intensity (measured in thousands of foot-candles).
P = (120 I) / (I^2 + I + 1)
For what light intensity is P a maximum?

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  1. p = (120i)/(i^2 + i + 1)
    dp/di = 120[(i^2+i+1)-i(2i+1)]/(i^2+i+1)^2
    where is that 0?
    where the numerator is zero (assuming the denominator is no 0 there)
    (i^2+i+1) = i(2i+1)
    0 = i^2 -1
    i^2 = 1
    i = +1 or -1
    if i = +1
    p = 120/3 = 40
    if i = -1, p = -120 (meaningless for negative intensity anyway)
    check the arithmetic, that is the method.

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  2. I=3

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