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Math Help - help please

  1. #1
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    help please

    okay so i have been given a question of :

    on the graph of y = 2x^3 -9x^2 - 12x - 7

    , the point (1, -2) is:

    a minimum , a max , neither but on the graph or not on the graph.

    So i have never done this before. Do i differentiate the equation and substitute values of x? Or is it a different way?

    Thanks People your help is appreciated.
    Last edited by the_sensai; August 20th 2008 at 05:18 PM. Reason: wrong equation
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  2. #2
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    skeeter's Avatar
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    does y = -2 when x = 1 ???
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  3. #3
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    Quote Originally Posted by the_sensai View Post
    okay so i have been given a question of :

    on the graph of y = 2x^3 -9x^2 - 12x - 7

    , the point (1, -2) is:

    a minimum , a max , neither but on the graph or not on the graph.

    So i have never done this before. Do i differentiate the equation and substitute values of x? Or is it a different way?

    Thanks People your help is appreciated.
    If the graph is for y = 2x^3 -9x^2 -12x -7,
    then point (1,-2) is not on the graph, because
    -2 = 2(1^3) -9(1^2) -12(1) -7
    -2 = -26 ----------not true.

    But if the graph were for y = 2x^3 -9x^2 +12x -7,
    Then point (1,-2) is on the graph.

    To check if (1,-2) is then a minimum, a maximum or neither, yes, you need to get the first derivative of y with respect to x. Then set dy/dx to zero.

    y = 2x^3 -9x^2 +12x -7
    dy/dx = 6x^2 -18x +12
    Set that to zero,
    0 = 6x^2 -18x +12
    Divide both sides by 6,
    0 = x^2 -3x +2
    0 = (x-1)(x-2)
    x = 1 or 2
    Meaning, when x=1 or x=2, the graph is minimum or maximum ....(or there is an inflection point).

    When x=1,
    y = 2x^3 -9x^2 +12x -7
    y = 2(1^3) -9(1^2) +12(1) -7
    y = 2 -9 +12 -7 = -2
    So, point (1,-2).

    Do you know how to check if (1,-2) is minimum or maximum?
    a) one way is find the dy/dx values when x is before and after x=1
    b) another way is to find the concavity of the graph by getting the second derivative at x=1.

    We do here the option b.
    dy/dx = y' = 6x^2 -18x +12
    d/dx(dy/dx) = y'' = 12x -18
    At x=1,
    y'' = 12(1) -18 = -6 ---------it is negative.
    Meaning, the the graph at x=1 is concaved downward.
    Meaning, the graph is a maximum there.
    Therefore, (1,-2) is a maximum point.
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  4. #4
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    thankyou so much that was a massive help.
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