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9.9 Using Second Derivatives

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Question 15

A marine engineer models the energy efficiency, EEE, of a prototype underwater turbine. The efficiency is measured in dimensionless units and depends on the flow velocity of the tide, vvv knots, according to the equation

E=24v−4v32−12,v>1. E = 24v - 4v^{\frac{3}{2}} - 12, \quad v > 1. E=24v−4v23​−12,v>1.

According to this model:

a.

find, using calculus, the maximum possible efficiency EEE.

[5]
b.

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

[3]
Markscheme

9.9 Using Second Derivatives Questions

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

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