(a) Show that y = 3a²x - x³ is strictly increasing for a < x < a and that on this interval y increases from -2a³ to 2a³. (b) By putting x = 2a sin and using the identity sin³ = (3 sin - sin 30)/4, show that the equation becomes y = 2a³ sin 36 and hence that x(y) = 2a sin -1 (1/7 sin-¹ (203)). 3

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