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Math Help - graphing a quartic

  1. #1
    Junior Member
    Joined
    Mar 2009
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    30

    Lightbulb graphing a quartic

    The equation of the graph is f(x)=X^4 -4x^3

    The x intercepts are at (0,0) and (4,0)

    The y-intercept is at (0,0)

    I found f'(x) to be 4x^3-12x^2, meaning the critical points are at (0,0) and (3,-27).

    Am I correct in saying that because its a quartic, there are no horizontal or vertical asymptotes?

    If so, it doesnt make sense when I graph it, I get a slanted N which intersects x in three places (-4,0), (0,0), (4,0).
    But when I enter the equation in an online graphing tool, [IMG]file:///C:/Users/NOORMA%7E1/AppData/Local/Temp/moz-screenshot.jpg[/IMG]I get a deep U.

    Am i doing something wrong?
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  2. #2
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
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    894
    correct it has no asymptotes. Also the reason why the looks diff is because you have to zoom out and then it will look like a U.
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