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Math Help - What are the stationary points for this function?

  1. #1
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    What are the stationary points for this function?

    Hello, I need help deriving this and finding the stationary points for the following:


     y= 3x / (x^2 + 1)

    If somebody could please show me the method of how to do this. I compared my answer with the result in a calculator and I do not know what I am doing wrong.
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by gva0324 View Post
    Hello, I need help deriving this and finding the stationary points for the following:


     y= 3x / (x^2 + 1)

    If somebody could please show me the method of how to do this. I compared my answer with the result in a calculator and I do not know what I am doing wrong.
    Hi gva0324.

    Use the quotient rule:

    \mbox{If}\ y=\frac uv,\ \frac{dy}{dx}=\frac{v\dfrac{du}{dx}-u\dfrac{dv}{dx}}{v^2}

    The stationary points are where \frac{dy}{dx}=0.
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  3. #3
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    Yes.

    I obtain 3 (x-1)^2 / (x^2 +1)

    Which seems to be wrong as the answer is

    3(1-x^2) / (x^2 + 1)

    How do I obtain the answer above?

    and using the answer what would be the stationary points?

    there are none?
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  4. #4
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by gva0324 View Post
    Yes.

    I obtain 3 (x-1)^2 / (x^2 +1)

    Which seems to be wrong as the answer is

    3(1-x^2) / (x^2 + 1)

    How do I obtain the answer above?

    and using the answer what would be the stationary points?

    there are none?
    The answer I got is \frac{3(1-x^2)}{(x^2+1)^2}. The stationary points are when this is 0 (there are two of them).
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