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Q7. (a) The volume of the square - based glass display case shown in Fig Q7(a) is 864 cm³.

The length of the base is x cm and the base is not made of glass.

Determine EACH of the following for the display case:

(i) an expression, in terms of x, for the area of glass, A cm², in the case; (4)

(ii) the dimensions of the case that minimize the amount of glass used;         (6)

(iii) the minimum area of glass used.        (2)

(b) Determine the first and second derivatives of the following function:

u = 3sinθ + (1 - 4 sin^2⁡θ)/(1 + 2sinθ) (4)