Question 1126376
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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
{{{v=x(5-2x)(7-2x)}}}
{{{algebra}}}{{{steps}}},...
...
{{{v=4x^3-24x^2+35}}}


Extreme values:
{{{dv/dx=12x^2-48x+35}}}

{{{12x^2-48x+35=0}}}


Using quadratic formula solution, x for extreme values for v may be
 x at  {{{(24+- sqrt(78))/12}}}.
One of these may work and the other one may not work.

.

.
The PLUS form is no good.


The MINUS form should work, for {{{x=1.264}}}.
Find v at x=1.264.
Max v, {{{highlight(13.97*inch^3)}}}.