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Math Help - function concave

  1. #1
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    function concave

    I'm sorry about my bad English, because I don't know the right expression for this, but I hope that you'll understand what I mean.
    What are the X's "values" which will make the following function "dwindling" f(X)=(2X-1)(X+3) I really hope that someone understands what I mean and can help me too. Thank you very very much.
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  2. #2
    MHF Contributor
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    Hi

    Do you mean decreasing ?
    Such as for x < y, f(x) > f(y)
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  3. #3
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    Hello, Fiona!

    I'll take a guess at what you meant . . .


    For for what x-values is: f(x) \:=\:\frac{2x-1}{x+3} a decreasing function?

    If we are allowed to use Calculus, determine when f'(x) \,<\,0.

    We have: . f\:\!'(x) \:=\:\frac{2\cdot(x+3) - (2x-1)\cdot1}{(x+3)^2} \;=\;\frac{7}{(x+3)^2}

    And we see that f\:\!'(x) is always positive.

    The function is never decreasing.



    The graph is even more convincing . . .
    Code:
                       *:       |
                        :       |
                      * :       |
                     *  :       |
                   *    :       |
                *       :       |
          *             :       |2
        - - - - - - - - + - - - + - - - - - - -
                        :       |            *
     -------------------+-------+-----*------------
                      -3:       *
                        :   *   |
                        : *     |
                        :       |
                        :*      |
                        :       |
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