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Q7. a. The cost, £P million, of laying 1000 m of pipe fora water main is given by:

P = 400/9A + 4A where A is the cross sectional area of the pipe in m².

i. Determine the cross-sectional area of the most economical pipe to use (8)

ii. Calculate the minimum cost of laying 1000 m of pipe (2)

b. Determine the coordinates and nature of the stationary points on the curve:

y = 2x³ - 24x - 32 (6)