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Q7(a), has a length of l cm and a capacity of 62.5 litres.

The triangular cross - section of the tank is right - angled and isosceles. with equal sides of length x cm. The tank is to be lined on the inside to make it watertight.

Determine EACH of the following for the tank:

i. the capacity in cm³; (1)

ii. An expression, in terms of x, for the surface area to be lined; (5)

iii. The value of x which minimizes the surface area to be lined. (4)

b. Determine the first and second derivatives of the function: Q = 12x³ + 8x + 6/x² (6)