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Math Help - Co-ordinates and a point C

  1. #1
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    Co-ordinates and a point C

    A question on my practice exam paper says:

    The curve C has equation y = x - 3x - 9x + 2. Find the coordinates of the stationary points of C and determine the nature of these points.

    I worked part out as:

    dy/dx = 3x - 6x - 9 = 0
    (/3) = x - 2x - 3 = 0
    (x-3)(x+1) = 0
    x = 3, x = -1

    When x=3:
    (3) - 3(3) - 9(3) + 2
    = 27 - 27 - 27 + 2
    = -25

    When x=-1:
    (-1) - 3(-1) - 9(-1) + 2
    = -1 - 3 + 9 + 2
    = 7

    Coordinates are (3,-25),(-1,7).

    Is this right so far and what do I need to do to complete the rest?
    Last edited by db5vry; December 5th 2008 at 05:38 PM.
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  2. #2
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    Quote Originally Posted by db5vry View Post
    A question on my practice exam paper says:

    The curve C has equation y = 3x - 3x - 9x + 2. Find the coordinates of the stationary points of C and determine the nature of these points.

    I worked part out as:

    dy/dx = 3x - 6x - 9 = 0
    (/3) = x - 2x - 3 = 0
    (x-3)(x+1) = 0
    x = 3, x = -1

    When x=3:
    (3) - 3(3) - 9(3) + 2
    = 27 - 27 - 27 + 2
    = -25

    When x=-1:
    (-1) - 3(-1) - 9(-1) + 2
    = -1 - 3 + 9 + 2
    = 7

    Coordinates are (3,-25),(-1,7).

    Is this right so far and what do I need to do to complete the rest?
    use the 2nd derivative test to determine if the points are maximums or minimums.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    use the 2nd derivative test to determine if the points are maximums or minimums.
    So if I had 3x - 6x - 9 I could use:

    dy / dx - which would be 6x - 6

    then substituting in the values, I would get:


    for x=3 - 18-6=12, so dy / dx < 0, meaning it is a maximum point


    and for x=-1, -6-6=-12, so dy / dx >0, meaning it is a minimum point?
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  4. #4
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    you typed them in backwards ...

    for x=3, 18-6=12, so dy / dx < 0, meaning it is a maximum point

    y'' > 0, not less


    and for x=-1, -6-6=-12, so dy / dx > 0, meaning it is a minimum point?

    y'' < 0, not greater
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