Let x cm be the length of a rectangular box. Then the dimensions of the box are shown as below. 9-x 2x 2x a) Show that the volume of the box can be written as V(x) = 4x²(9 – x). b) Copy and fill in the table: -3 0. 3 6. 10 V(x) c) Sketch the volume function. d) What is the domain of the function i) in general? ii) for this context? e) What is the range of the function i) in general? ii) for this context? e) Estimate the length that gives the maximum volume?

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