Posted by Mely on Saturday, July 31, 2010 at 9:51pm.
An open box is to be made from a 21 ft by 56 ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have.

calculus  drwls, Sunday, August 1, 2010 at 6:45am
Let x be the length of the side of the square taken off each corner. The open box will have length 562x, width 212x and height x.
The volume of the box is
V(x) = x(562x)(212x)
Set the derivative dV/dx equal to zero and compute the corresponding x. Use that to compute the maximum volume.
Someone will gladly critique your work if you show what you did and need additional assistance.
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