A square sheet of metal of side a has squares cut on all its corners and the sides bent to form an open box. What is the maximum volume of the box?
The sheet of metal we have has sides equal to a. Let the sides of the squares that are cut from all the corners be x.
Now we have a length equal to a – 2x, to fold on all the sides and create the box.
The volume of the box is (a – 2x)^2*x = (a^2 + 4x^2 – 4ax)*x
V = a^2x + 4x^3 – 4ax^2
To maximize V, we...
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