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Differentiation

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Question 507

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

Differentiation Questions

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

717 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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