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Math Help - Stationary points - find horizontal line

  1. #1
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    Stationary points - find horizontal line

    (I apologise if this is in the incorrect section)

    I have a stationary points question that I really do not get. I have worked out that the SP's are (0,0) and (2,-4), but I do not know how to find Q.

    Question:
    Part of the graph of the curve with equation y=3x^2-x^3 is shown below.

    Stationary points - find horizontal line-diagram.png
    (I used a graphic calculator online to draw the graph)

    a) Establish the coordinates of the stationary point P.
    b) The horizontal line through P meets the curve again at Q. Find the co-ordinates of Q.

    So far, I have worked out the SPs:

    y=3x^2-x^3
    \frac{dy}{dx}=6x-3x^2
    -3(x-2)=0
    -3x=0 or x-2=0
    x=0 or x=2

    When x=0, y=0, point(0,0)
    When x=2, y=3(2)^2-3^3=4 point(2,4) (which is P).

    But I don't know how I'm supposed to find Q. Can anyone please help?

    Thanks in advance
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  2. #2
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    Re: Stationary points - find horizontal line

    Quote Originally Posted by watp View Post
    b) The horizontal line through P meets the curve again at Q. Find the co-ordinates of Q.
    But I don't know how I'm supposed to find Q. Can anyone please help?
    Solve 4=3x^2-x^3. That will give (x,4)
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  3. #3
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    Re: Stationary points - find horizontal line

    Quote Originally Posted by Plato View Post
    Solve 4=3x^2-x^3. That will give (x,4)
    Thanks! I never knew it would be that simple
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