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Math Help - Area and Perimeter

  1. #1
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    Area and Perimeter

    Rectangle in first quadrant has one vertex at origin and opposite vertex on the curve y=8/(1+x^2). Show the rectangle with max area isn't the same as the rectangle with max perimeter.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Area and Perimeter

    I would begin by stating the area and perimeter functions. Can you state these?
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  3. #3
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    Re: Area and Perimeter

    area: 2x(8/1+x^2)

    Perimeter: 4x+ 2(8/1+x^2)
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Area and Perimeter

    One vertex is at (0,0) and the other is at (x,y) (on the given curve) where x and y are positive. So we have:

    Area: xy

    Perimeter: 2(x+y)

    Do you see that you have doubled x? Now substitute for y using the definition of the given curve.
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  5. #5
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    Re: Area and Perimeter

    then what would you do after youve substituted it in?
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Area and Perimeter

    Once we have the area and perimeter as a function of x alone, then equate the derivatives to zero to find the critical numbers. Use an appropriate test to ensure you have maximized the two functions.
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