Question: QUESTION 1 [TOTAL: 20 MARKS] (a) An open box shown below is made from a piece of rectangular card with dimensions of 64 cm and

QUESTION 1 [TOTAL: 20 MARKS] (a) An open box shown below

QUESTION 1 [TOTAL: 20 MARKS] (a) An open box shown below is made from a piece of rectangular card with dimensions of 64 cm and 24 cm. A square side of length x cm is cut out from each corner so that the box can be made by folding. 24cm 64cm (i) Find the equation of volume, V, of the box in terms of x. [3 marks] (1i) Differentiate the volume equation found in part (i). [2 marks] (111) Find the value of x in which may produce a maximum or minimum of V. [4 marks] (iv) Find the value of I and justify whether Vis a maximum or minimum. [5 marks] ( b ) By letting u = 4 + 3x-, find S 2x (4+ 3x3)2 dx. [6 marks]

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