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Homework Help: Optimization of Area; Inscribed Rectangles

  1. Nov 4, 2013 #1


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    Gold Member

    1. The problem statement, all variables and given/known data

    http://i.minus.com/jbkHm5oH1LfQ1k.png [Broken]

    2. Relevant equations

    The area of a rectangle is its base times its height.

    3. The attempt at a solution

    The rectangle is inscribed. Its area is 2xy. I can substitute in the equation of the semicircle to get rid of the y-term in my area equation. I can then differentiate with respect to x and find what zeros the derivative (or causes the derivative not to exist) and test the points I find that are on the domain of x (0 to square root of 12).

    I find x = sqrt6 as that point that maximizes area and therefore the dimensions must be 2sqrt6 and sqrt6.

    http://i.minus.com/jFWGaWoQsb5FX.jpg [Broken]
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 4, 2013 #2


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    Looks right to me.
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