p = 120 i / (i^2 + i + 4)
dp/di = 0 at max or min
0 = [(i^2 + i + 4)120 - 120 i(2i+1)]/(i^2 + i + 4)2
look for zeros of numerator
0 = 120 i^2 +120 i + 480 -240 i^2 -120 i
0 = -120 i^2 +480
i^2 = 4
i = 2
The rate (in mg carbon/m^3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function
P = (120I)/(I^2 + I + 4)
where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
1 answer