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).

Question

P = (120 I) / (I^2 + I + 1)
For what light intensity is P a maximum?

Answer 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.

Answer 2

I=3