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Q7. The weekly profit, £P, of a microbrewery is given by

P = 120x - 0.4x², where x is the number of barrels of beer produced.

Determine EACH of the following:

(i) the number of barrels of beer to produce per week to maximise the profit. (6)

(ii) the maximum weekly profit. (2)

(b) Given H = 4 t² + log_e⁡ t - 2/t determine EACH of the following.

(i) dH/dt (4)

(ii) d² H/dt² (4)