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Math Help - Help with partial derivatives

  1. #1
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    Arrow Help with partial derivatives

    Hello,
    I need to find the stationary points and classify them

    f(x,y)=\frac{xy}{1+x^2}

    This is how I did it:

    (1) f_x(x,y)=\frac{y(1-x^2)}{(1+x^2)^2}
    (2) f_y(x,y)=\frac{x}{1+x^2}

    (2) yields that x=0

    and (1) that y=0 or x=-1, x=1

    So that I have 3 stationary points. But apparently the answer is that the only stationary point is (0,0); which I could get if I insert x=0 in (1). But the problem is that I don't understand why x=-1 and x=1 aren't valid solutions.
    Last edited by mr fantastic; September 20th 2009 at 12:54 AM. Reason: Corrected the notation
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  2. #2
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    Quote Originally Posted by sebasto View Post
    Hello,
    I need to find the stationary points and classify them

    f(x,y)=\frac{xy}{1+x^2}

    This is how I did it:

    (1) f_x(x,y)=\frac{y(1-x^2)}{(1+x^2)^2}
    (2) f_y(x,y)=\frac{x}{1+x^2}

    (2) yields that x=0

    and (1) that y=0 or x=-1, x=1

    So that I have 3 stationary points. But apparently the answer is that the only stationary point is (0,0); which I could get if I insert x=0 in (1). But the problem is that I don't understand why x=-1 and x=1 aren't valid solutions.
    Both equations have to be satisfied simultaneously. Does x = \pm 1 satisfy equation (2)?
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