The rate (img carbon/m3/h) which photosynthesis takes place for a species of phytoplankton is modeled by the function. P = 100L/( L2 + L + 4), L = Light intensity. what light intensity is P a max?

Question

I have no clue how to even attempt this problem we are learning optimization problems at the moment.

Answer 1

The question is asking you to find the value of L at dP/dL = 0

Given P = 100L/(L² + L + 4). using your preferred method of differentiation, you get

dP/dL = 100/((L² + L + 4) -100L(2L+1)/(L² + L + 4)² = 0

= [100(L² + L + 4) - 200L² -100L]/(L² + L + 4)² = 0

= (-100L² + 400)/(L² + L + 4)² = 0

==> L = 2