SOLUTION: What is the maximum volume of a open box created from a square of side length 24? Keep in mind that V=LWH. So for this problem the dimensions are as follows: L = 24-2x, W = 24-2x

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Question 628271: What is the maximum volume of a open box created from a square of side length 24? Keep in mind that V=LWH. So for this problem the dimensions are as follows:
L = 24-2x, W = 24-2x and H = x. The maximum volume will be where the volume equation is the greatest.
You are to determine:
1. The volume equation.
2. The maximum volume.
3. The value of x that maximizes the volume
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is the maximum volume of a open box created from a square of side length 24? Keep in mind that V=LWH. So for this problem the dimensions are as follows:
L = 24-2x, W = 24-2x and H = x. The maximum volume will be where the volume equation is the greatest.
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V+=+%2824-2x%29%5E2%2Ax+=+4x%5E3+-+96x%5E2+%2B+576x
dV%2Fdx+=+12x%5E2+-+192x+=+0
x = 4
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V(4) = 256 cubic units
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