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Math Help - Differentiation

  1. #1
    Member Awsom Guy's Avatar
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    Differentiation

    Find the slope of the curve y= (x)/(x^2+1) at the origin. Find the equation of the tangent and of the normal at the origin.

    Is this how I find y:
    y= (0)/(0^2+1)
    =0
    where I have place x=0

    I cannot attempt this as I have no idea where to start this question. I think I do not understand this question. Thanks.
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  2. #2
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    Quote Originally Posted by Awsom Guy View Post
    Find the slope of the curve y= (x)/(x^2+1) at the origin. Find the equation of the tangent and of the normal at the origin.

    Is this how I find y:
    y= (0)/(0^2+1)
    =0
    where I have place x=0

    I cannot attempt this as I have no idea where to start this question. I think I do not understand this question. Thanks.
    You should know how to find the equation of a tangent.

    Find the derivative, evaluate it at x = 0. Substitute into y = mx + c to find the y intercept.


    For the normal, remember that m_1m_2 = -1 for perpendicular lines.
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  3. #3
    Member Awsom Guy's Avatar
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    If this is the derivation: (x^2-1)/(x^2+1)^2
    then if I nake x=0 and do this:
    (0-1)/(0^2+1)(0^2+1)
    =-1/1
    =-1
    Does this find the y co-ordinate or the gradient.
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  4. #4
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    Quote Originally Posted by Awsom Guy View Post
    If this is the derivation: (x^2-1)/(x^2+1)^2
    then if I nake x=0 and do this:
    (0-1)/(0^2+1)(0^2+1)
    =-1/1
    =-1
    Does this find the y co-ordinate or the gradient.
    Close, but the derivative is actually \frac{1 - x^2}{(x^2 + 1)^2} (found using the Quotient Rule).

    After you substitute x = 0, you have the GRADIENT of the tangent.
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  5. #5
    Member Awsom Guy's Avatar
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    Now how do I place that onto the y=mx+b formula, the gradient is 1. So it is y=1x+b. How do i find y, do I make y=0.
    Thanks
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  6. #6
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    Quote Originally Posted by Awsom Guy View Post
    Now how do I place that onto the y=mx+b formula, the gradient is 1. So it is y=1x+b. How do i find y, do I make y=0.
    Thanks
    You have already found that the point (x, y) = (0, 0) lies on the curve. If the gradient is 1, then m = 1.


    Put these three values into the equation y = mx + c and find c.
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  7. #7
    Member Awsom Guy's Avatar
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    oh ok thanks
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  8. #8
    Member Awsom Guy's Avatar
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    so that maks it y=1x
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  9. #9
    Member Awsom Guy's Avatar
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    just checking something, to calculate the normal do I inverse it and make it negative in this case 1/-x but just so you know it isn't 1/-x it is just -x.
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  10. #10
    Member Awsom Guy's Avatar
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    and how did you find x=0 and y=0, thanks
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  11. #11
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    Quote Originally Posted by Awsom Guy View Post
    and how did you find x=0 and y=0, thanks
    Reread your original question and what you posted... You answered this part of the question yourself.
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