1. ## 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

2. This is how your graph looks like. It DOES tend to positive infinity.

3. but that is not the graph that was given to me looked like!

4. 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.