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MATH1025 Introduction to Mathematics and StatisticsAssignment 3 - Due Wednesday, 14 November, In ClassNAME:STUDENTID:Section:1. (10 marks) We build a chocolate box which has 4 cubical containers of dimensionx×x×h. The totalmaterial isf(x, h) = 4x2+12xhand the volume is 4x2h. Assume the volume is 4, what geometry producesthe minimal cost?
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2. (10 marks) A rectangle with corners at (-x,0),(x,0),(x, y),(-x, y) is inscribed in a half circlex2+y2= 1wherey≥0 is in the upper half plane. Assume we movexasx(t) =t2. Find the rate of change ofy(t).