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Math Help - Graphing help

  1. #1
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    Exclamation Graphing help

    my question gives me a graph that is f'(x) of the function f and asks me to graph f"(x) and a possible f(x)...and i cannot graph f"(x) without knowing the equation of the given graph right? so i was trying to figure out the equation. and it was fairly straight forward because it had roots andwas a polynomial, but at the end (right side) it did not go to positive infinity, but came down towards the x axis...and continued like that off the page..so i assumed it was a horizontal asymptote but if it does not affect the graph much, i could ignore it.

    this is the equation i came up with: x(x-2)^2(x-4)(x+2)

    but after the last root (4) the graph goes up and thn comes back down and there is a horizontal asyptote at y=0 as x approaches infiinity. how would i show that in the equation?

    the graph i have been given, after it rises above the x-axis at x=4, it goes up for some length, then drops back down after x=5,and keeps decreasing, but never equals/passes the x-axis/0...so would that not be a horizontal asymptote? I just want to know how that would be stated within my polynomial equation that i got.

    like i think im supposed to use exponential functions (e^x or e^-x) but how would i state that in the equation
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  2. #2
    Senior Member Sambit's Avatar
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    This is how your graph looks like. It DOES tend to positive infinity.
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  3. #3
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    but that is not the graph that was given to me looked like!
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  4. #4
    Senior Member
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    Did the graph look anything like the graph in the following link?

    I looked around for a function that would work better than e^(-x). e^(-x) will work, but the relative max between x=-2 & x=0 is huge compared the other extrema. So I shifted & flipped the tanh function --- hyperbolic tangent.
    Last edited by SammyS; April 21st 2011 at 05:41 AM.
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