Calculus Calculus Math Forum

 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 6in×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. $V =x(6-2x)(16-2x) =4x(3-x)(8-x) = 4(3x-x^2)(8-x)$ $\dfrac{dV}{dx}=4\bigg[(3x-x^2)(-1) + (3-2x)(8-x)\bigg]$ $\dfrac{dV}{dx} = 4(3x^2-22x + 24) = 4(3x -4)(x-6) = 0$ $x= \dfrac{4}{3}$ is the only valid solution. Why? Tags application, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post ILoHateMath Trigonometry 2 July 18th, 2016 06:36 PM mathman225 Trigonometry 5 May 14th, 2011 02:26 PM David_Lete Algebra 3 March 5th, 2009 07:16 AM incarnate Algebra 4 November 3rd, 2008 06:09 AM

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