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 July 17th, 2009, 02:30 PM #1 Newbie   Joined: Jul 2009 Posts: 1 Thanks: 0 Maximum area of an area within y=x^2 I've got this problem that I'm trying to solve, I've been twisting my brain for several hours now. An area 'A' is limited by the curve y=x^2, the x-axel and the line x=2 In this area is a rectangle with the area R, as seen in the figure. Calculate the maximum relation between R and A in exact form. If someone could take a look at this and help me, I would appreciate it very very much! (sorry for my bad english) July 17th, 2009, 03:48 PM   #2
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Re: Maximum area of an area within y=x^2

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 Originally Posted by media12 I've got this problem that I'm trying to solve, I've been twisting my brain for several hours now. An area 'A' is limited by the curve y=x^2, the x-axel and the line x=2 In this area is a rectangle with the area R, as seen in the figure. Calculate the maximum relation between R and A in exact form. If someone could take a look at this and help me, I would appreciate it very very much! (sorry for my bad english)
The height of the rectangle is y, the width is 2-x. Since y=x^2, the area is 2x^2 - x^3. Take derivatives and get extrema at 4x - 3x^2. The solutions are x=0 (min) and x=4/3 (max). At max, y=16/9, so area = 32/27.
The area under the parabola is 8/3 (I'll let you derive it). Tags area, maximum, yx2 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 PlzzHelp Algebra 2 December 5th, 2013 09:45 AM zerostalk Algebra 6 January 10th, 2012 08:06 PM gus Algebra 1 April 17th, 2011 04:25 PM GVDave2012 Calculus 1 December 11th, 2010 06:27 PM brunojo Algebra 2 November 16th, 2007 10:30 AM

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