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Year 12 Methods (Unit 3 & 4) The second derivative and applications

Optimisation problems

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Question 1
10264

A box is made from an 8\(~\text{cm}\) by 4\(~\text{cm}\) rectangle or cardboard by cutting out 4 equal squares of side \(x~\text{cm}\)  from each corner. The edges are turned up to form a box. The volume of the box \(V\) is given by the formula?

\(V = 4{x^3} - 24{x^2} + 32x\)

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