The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function

Question

P = (80i) / i^2 + i + 1

where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?

I = ?

Answer 1

To find critical point(s) you need to use equality of P'(x) =0 that gives:

 dP/di= 80(1-i^2)/(i^2 +i+1)^2=0 at x=1;

 Then, to state that at x=1 the function will have its maximum you need to show that P'' (x=1) <0.

The shorter way is to draw the graph of P(i) that shows maximum value  at x=1