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Math Help - If the f(1)= 4

  1. #1
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    If the f(1)= 4

    If f(1) = 4 , f(2)=5, f(7) = 5 and f(8)=4, find the value of f(6).Also obtain the value of x for which f(x) is maximum or minumum.

    I don't have a clue what to do

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  2. #2
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    Is this the complete problem? I mean f(6) can be anything really; I am also assuming you are meant to notice that f(x) is continuous, and thus a local maximum must occur between f(5) and f(7) - or hell f(5) and f(7) could be the local maximum and the graph dips btween f(5) and f(7). I dunno, theres a lot that can be going on here. Is this all the information - was there a picture to go along with this question?
    Last edited by mr fantastic; January 3rd 2010 at 02:47 AM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by wolfyparadise View Post
    If f(1) = 4 , f(2)=5, f(7) = 5 and f(8)=4, find the value of f(6).Also obtain the value of x for which f(x) is maximum or minumum.

    I don't have a clue what to do

    Nor, do the rest of us, please post the entire question.

    CB
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  4. #4
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    sorry but this is the question which i posted is what i have , i also am having daoubt about the question thats why i posted it in the forum
    please let em knw is any body can figure it out
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  5. #5
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    Hello, wolfyparadise!

    It is a carelessly-worded problem.
    As stated, there is an infinite number of possible answers.


    If f(1) = 4,\;f(2)=5, f(7) = 5,\;f(8)=4
    Find the value of f(6).
    Also find the value of x for which f(x) is maximum or minumum.
    Graph the given points . . .

    Code:
          |
        5 +       *         *
          |       :         :
        4 +   *   :         :   *
          |   :   :         :   :
          |   :   :         :   :
          |   :   :         :   :
      . . + - + - + - - - - + - + - - - - -
          |   1   2         7 - 8
          |

    From the symmetry, I would guess that
    . . we are expected to assume f(x) is a parabola.

    The general parabola is: . f(x) \:=\:ax^2 + bx + c

    And we can determine that: . a = -\tfrac{1}{7},\;b = \tfrac{10}{7},\;c = \tfrac{19}{7}

    Hence, the function is: . f(x) \;=\;-\tfrac{1}{7}x^2 + \tfrac{10}{7}x + \tfrac{19}{7}

    Now you can answer their question . . .

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