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:
find, using calculus, the maximum possible efficiency EEE.
Justify, also using calculus, that the efficiency you have found is a maximum.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 327 questions covering 12.1 Gradients of Curves, 12.2 Differentiation from first principles, 12.3 Differentiating x^n, 12.4 Differentiating Quadratics, 12.5 Differentiating functions with two or more terms, 12.6 Gradients, Tangents and Normals, 12.7 Increasing and Decreasing Functions, 12.8 Second Order Derivatives, 12.9 Stationary Points, 12.10 Sketching Gradient Functions, and 12.11 Modelling with Differentiation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
