February 15th, 2017, 03:50 AM  #1 
Member Joined: Aug 2016 From: South Korea Posts: 55 Thanks: 0  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 03:17 PM. 
February 15th, 2017, 04:22 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 3,094 Thanks: 1677 
I'm assuming the original rectangular sheet is 6 by 16 ... you state it's 6 by 6. $V =x(62x)(162x) =4x(3x)(8x) = 4(3xx^2)(8x)$ $\dfrac{dV}{dx}=4\bigg[(3xx^2)(1) + (32x)(8x)\bigg]$ $\dfrac{dV}{dx} = 4(3x^222x + 24) = 4(3x 4)(x6) = 0$ $x= \dfrac{4}{3}$ is the only valid solution. Why? 

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