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Q7. (a) The rate at which a particular ship’s engine consumes fuel is given by:

rate = 30 + 0.002v³ tonnes per hour (where v is the speed of the ship in km/hr).

Calculate EACH of the following:

(i) the speed at which the minimum amount of fuel is used on a voyage of 1500 km; (10)

(ii) the minimum amount of fuel for the journey. (2)

(b) Determine the first derivative of the following function: (4)

R = h + 4√h - 3/(2√h) + 1/h