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Applying the Derivative

  1. May 28, 2009 #1
    1. Find two numbers x and y whose sum is 120 and whose product is a maximum.



    2. none



    3. x + y = 120
    xy = maximum
    x = 120 - y
    I wrote these down but I don't know what to do next. Can you please show me? :) Thank You!!
     
  2. jcsd
  3. May 28, 2009 #2

    danago

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    Gold Member

    Well you have the function P = xy which you want to maximize, however it contains two variables. Are they independent though? How can you reduce this function down to a single variable function?
     
  4. May 29, 2009 #3

    HallsofIvy

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    Staff Emeritus
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    Replace the x in xy with 120- y so you have only one variable. Now, do you know how to "apply the derivative" to find where a function has a maximum or minimum?
     
  5. May 29, 2009 #4

    Mark44

    Staff: Mentor

    As an alternate approach, the graph of your area function, as a function of either x or y alone, is a parabola. You can find the vertex of the parabola, at which the maximum area is attained, without using calculus.
     
  6. May 29, 2009 #5

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Ah! Excellent point.
     
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