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 9.9 Using Second Derivatives with exam-style questions for A Level Maths. 57 questions, 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.