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Find the greatest value of function

  1. May 2, 2012 #1
    1. The problem statement, all variables and given/known data
    If x + y = 60 and x,y >0 find greatest value of x( y-30)^2


    2. Relevant equations



    3. The attempt at a solution
    I did this by the usual method that is by substituting 60 - x for y and then differentiating the function and equating derivative to zero.
    I got x = 10 and x=30. At x=30 value is zero and at x=10 value is 4000 so my answer was 4000
    But i checked the solution it says that greatest value does not exist
    It gave the hint that limit x-->60(-) f(x) = 54000 so greatest value does not exist

    I'm lost here because the fucntion ought to have some greatest value. Help!
     
  2. jcsd
  3. May 2, 2012 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    hi jd12345! :smile:
    sketch the graph …

    it has a local maximum at 10, a local minimum at 30, at keeps increasing above 30

    it is only defined on (0,60) (not [0,60]), so it never reaches the value it would have at 60 ! :wink:
     
  4. May 2, 2012 #3
    Ok it maeks sense now - thank you
     
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