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Max/Min Problems

  1. Oct 30, 2008 #1
    1. The problem statement, all variables and given/known data
    A rectangle is bounded by the X-axis and the semicircle Y = [(sqrt)36-x^2]. What dimensions should the rectangle have so that its area is a maximum.


    2. Relevant equations

    Just a note, the 36-x^2 is all under the radical.

    3. The attempt at a solution

    Ditto.
     
  2. jcsd
  3. Oct 30, 2008 #2

    gabbagabbahey

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    Well, the width of the rectangle is clearly [itex]2x[/itex], and its height is [itex]y=\sqrt{36-x^2}[/itex]....so what is its area [itex]A(x)=?[/itex] for a given value of [itex]x[/itex]? How do you find the maximum of such a function?

    P.S. I don't think the definition of "ditto" is exactly what you seem to think it is (just a friendly FYI)
     
  4. Oct 30, 2008 #3
    Wouldn't I just find the area by multiplying both of them together?
     
  5. Oct 30, 2008 #4

    gabbagabbahey

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    Sounds good to me; the last time I checked the area of a rectangle was just width times height ;0)
     
  6. Oct 30, 2008 #5
    So I multiply them together then take the derivative, and then find the critical points of that?
     
  7. Oct 30, 2008 #6

    HallsofIvy

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    Yes, now do it!
     
  8. Oct 30, 2008 #7
    Done.

    Many thanks.
     
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