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1.10 G: Differentiation

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Question 138

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

1.10 G: Differentiation Questions

  1. A Level
  2. /Maths
  3. /1.10 G: Differentiation

375 exam-style questions on AQA A Level Maths 1.10 G: Differentiation, covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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