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.
