SOLUTION: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides A)Suppose the paper is 5"-wide by 7"-long. I)What is the maximum volume for

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Question 1126376: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides
A)Suppose the paper is 5"-wide by 7"-long.
I)What is the maximum volume for the box?
ii)What is the maximum volume for the box?
B)Suppose we instead create the box from a 7"-wide by 9"-long sheet of paper.
I)What is the maximum volume for this box?
ii)What cutout length produces the maximum volume?

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
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A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides
A)Suppose the paper is 5"-wide by 7"-long.
I)What is the maximum volume for the box?
ii)What is the maximum volume for the box?
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v, volume
x, length of square to remove at each corner

,...
...


Extreme values:



Using quadratic formula solution, x for extreme values for v may be
x at .
One of these may work and the other one may not work.
.
.
The PLUS form is no good.

The MINUS form should work, for .
Find v at x=1.264.
Max v, .

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