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February 15th, 2017, 02:50 AM   #1
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Post Application Problem

I'm reviewing for our exam tomorrow so I want to ask how they got the answer
x = 6inches
x = 1.3inches

to the problem:

An open rectangular box is to be made from 6inĂ—6in rectangular piece of cardboard by cutting identical squares from its corners and turning up the sides. Find the volume of the largest box that can be formed.

and this is my solution:

16754270_1322071531184015_63778220_n.jpg

What should I do next to get x = 6in and x = 1.3in ??

Last edited by skipjack; February 15th, 2017 at 02:17 PM.
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February 15th, 2017, 03:22 AM   #2
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I'm assuming the original rectangular sheet is 6 by 16 ... you state it's 6 by 6.

$V =x(6-2x)(16-2x) =4x(3-x)(8-x) = 4(3x-x^2)(8-x)$

$\dfrac{dV}{dx}=4\bigg[(3x-x^2)(-1) + (3-2x)(8-x)\bigg]$

$\dfrac{dV}{dx} = 4(3x^2-22x + 24) = 4(3x -4)(x-6) = 0$

$x= \dfrac{4}{3}$ is the only valid solution. Why?
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