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.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
