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Q7. A ship sailing at v knots consumes fuel at a rate of (1.5 + 0.001v³) tonnes per hour.

Determine EACH of the following for this ship when it completes a passage of 2000 nautical miles at a speed of v knots:

(i) the speed which gives the greatest fuel economy; (10)

(ii) the minimum amount of fuel consumed. (3)

(b) Given y = √x/2 - 2/√x determine dy/dx. (3)