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Q7. (a) The cost, in £ millions per day, of pumping oil from an offshore oil terminal is related to the radius of the pipe carrying the oil.

For a pipe of radius r metres the cost is given by C = r + 4/r + 0.5

Calculate EACH of the following:

(i) the radius of pipe which minimises the cost; (6)

(ii) the minimum cost per day. (2)

(b) y = 10x^0.4 + e^2x – 60√x

Determine EACH of the following:

(i) dy/dx                              (4)

(ii) (d² y)/dx²                   (4)