Question: Show work. A box with a square base and open top must have a volume of 48668 cm. We wish to find the dimensions of

Show work. A box with a square base and open top

Show work.

A box with a square base and open top must have a volume of 48668 cm". We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only 2, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of c. ] Simplify your formula as much as possible. A(x) Next, find the derivative, A'(x). A'(x) Now, calculate when the derivative equals zero, that is, when A'(2) = 0. [Hint: multiply both sides by x . ] A'(=) = 0 when c

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