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Differentiation

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Question 540

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>0

where III is the light intensity delivered to the colony in kilolux.

According to this model:

a.

find, using calculus, the maximum possible rate of oxygen evolution.

[4]
b.

Justify, also using calculus, that the rate you have found is a maximum.

[3]
Markscheme

Differentiation Questions

  1. A Level
  2. /Maths
  3. /Differentiation

649 exam-style questions on Edexcel A Level Maths Differentiation, 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. Each one has a worked solution and a mark scheme showing where the marks go.

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