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Math Help - word problem (rectangular)

  1. #1
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    word problem (rectangular)

    a rectangular has one vertex(corner) at (0,0) and the diagonally opposite vertex(corner) in the first quadrant on the curve of the function y = 1/(1+x^2). find the dimensions of the rectangle with the largest area.

    how do i do this question?

    would area be a = (2x)(1/(1+x^2)) ?
    Last edited by haebinpark; March 25th 2010 at 04:57 PM.
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  2. #2
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    Quote Originally Posted by haebinpark View Post
    a rectangular has one vertex(corner) at (0,0) and the diagonally opposite vertex(corner) in the first quadrant on the curve of the function y = 1/(1+x^2). find the dimensions of the rectangle with the largest area.

    how do i do this question?
    first, and most important, make a sketch.

    then write the area as a function of x ...

    A = xy = \frac{x}{1+x^2}

    now find \frac{dA}{dx} and maximize like you were taught.
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  3. #3
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    do i find derivative of a = 1/(1+x^2)?
    not derivative of a = (2x)(1/(1+x^2))?
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  4. #4
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    Quote Originally Posted by haebinpark View Post
    do i find derivative of a = 1/(1+x^2)?
    not derivative of a = (2x)(1/(1+x^2))?
    once again with more clarity ...

    the area of the rectangle in quad I is A = x \cdot \frac{1}{1+x^2} = \frac{x}{1+x^2}
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