A marine biologist is investigating the metabolic activity of a specific phytoplankton colony in a controlled bioreactor. The rate of oxygen evolution, RRR, measured in micromoles per second (μmol s−1\mu\text{mol s}^{-1}μmol s−1), is modelled by the function
R=54I−4I32−120,I>0 R = 54I - 4I^{\frac{3}{2}} - 120, \quad I > 0 R=54I−4I23−120,I>0where III is the light intensity delivered to the colony in kilolux.
According to this model:
find, using calculus, the maximum possible rate of oxygen evolution.
Justify, also using calculus, that the rate you have found is a maximum.
