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Maximum Area Problem

  1. Oct 30, 2009 #1
    1. David has 400 yrs of fencing and wishes to enclose a rectangular area. a) express the area A of the rectangle as a function of the width w of the rectangle. b) For what value of w is the area largest. c) What is the maximum area?



    2. A=xy... My teacher does not want us to use derivatives.



    3. I cant even being to attempt it.
     
  2. jcsd
  3. Oct 30, 2009 #2

    ideasrule

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    You got A=Lw and you want the area in terms of w, so the next step is to figure out what L is (in terms of w) and sub it into A=Lw.

    Hint: use the perimeter formula
     
  4. Oct 30, 2009 #3
    So does that mean L=400-w?
     
  5. Nov 3, 2009 #4

    LCKurtz

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    No. Draw a picture and label all 4 sides L or w. What is it that equals 400?
     
  6. Nov 4, 2009 #5
    It may help to think of it this way:

    What is greater?

    (x-n)(x+n)
    or
    x2

    To help, what is another way of writing the first one?


    What's to say you can't use optimisation (derivatives) to check your answer?
     
  7. Nov 4, 2009 #6

    HallsofIvy

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    There would be no reason to use derivatives. The function to be optimized is a quadratic and completing the square works nicely.
     
  8. Nov 4, 2009 #7

    Mark44

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    That's going to take him a very long time!:wink:
     
  9. Nov 8, 2009 #8

    tiny-tim

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    :wink: He probably means light-years! :biggrin:
     
  10. Nov 8, 2009 #9

    Mark44

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    As opposed to heavy years?:biggrin:
     
  11. Nov 9, 2009 #10
    Nah, I would have thought dark years
     
  12. Nov 9, 2009 #11

    tiny-tim

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    ah … dark time

    that mysterious phenomenon which is generally interspersed among ordinary time, but occasionally is more concentrated, causing effective time to pass more slowly and more heavily. :wink:
     
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