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9.9 Using Second Derivatives

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Question 43

A marine biologist is investigating the metabolic activity of a specific phytoplankton colony in a controlled bioreactor. The rate of oxygen evolution, $R$ , measured in micromoles per second ( $s−1\mu\text{mol s}^{-1}$ ), is modelled by the function

4I^{\frac{3}{2}} - 120, \quad I > 0

where $I$ is the light intensity delivered to the colony in kilolux.

According to this model:

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

[4]

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

[3]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.

9.9 Using Second Derivatives

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9.9 Using Second Derivatives

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Question 43

4I^{\frac{3}{2}} - 120, \quad I > 0

where $I$ is the light intensity delivered to the colony in kilolux.

According to this model:

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

[4]

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

[3]

Markscheme

9.9 Using Second Derivatives Questions

A Level
Maths
9.9 Using Second Derivatives

57 exam-style questions on Edexcel A Level Maths 9.9 Using Second Derivatives. Each one has a worked solution and a mark scheme showing where the marks go.