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A square sheet of paper \(10 \,\mathrm{cm}\) by \(10 \,\mathrm{cm}\) is made into an open box (no top) by cutting out squares of side \(x\) cm at each corner and folding up the sides.
  1. Write an expression for the volume \(V\) of the box in terms of \(x\).
  2. Find the value of \(x\) that maximizes the volume (verification with the second derivative test is optional).

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