If a function goes to negative infinity but has crests and dips in it, is there a lowest point on the graph, or is the lowest point undefined, or negative infinity?

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If a function goes to negative infinity but has crests and dips in it, is there a lowest point on the graph, or is the lowest point undefined, or negative infinity?

Mathematics
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whats the function?
1 sec
|dw:1434750076795:dw| something like this?

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Other answers:

I think so yes..
\[-577 + 736 x - 324 x^2 + 60 x^3 - 4 x^4\]
well it doesn't have a absolute min
you are looking at a polynomial ?
polynomials don't have vertical asymptotes
I guess you are talking about the end behavior of the graph maybe
when you talk about going to negative infinity ?
anyways to find the lowest point I would first differentiate your polynomial there if I were you
then find critical numbers by finding when f'=0
I see something like this.. and the question asks, is there a lowest point on the graph? |dw:1434750324649:dw| but I see two - infinity's on the ends.. and this middle trough.. and was wondering.. is that considered a low point? or are the low points considered undefined?
are you looking for local min?
or absolute min?
as you said there is no absolute min because the end behavior of the graph goes to neg infinity
That might be my answer then...
is there an interval for which you are to restrict this function to?
the actual question was this.. I found the high point no problem, and the trough.. Find the highest point on the graph of f[x] = -577 + 736 x - 324 x^2 + 60 x^3 - 4 x^4 . Is there a lowest point on this graph? but then couldnt remember how low points, were defined..
something I should have remembered from high school I guess.. but then couldnt find even anything on google that answered that directly.
well I think lowest point is absolute min
but there are lowest points on smaller intervals of the graph
the lowest point is the lowest point on the graph, which is negative infinity :)
@dan815 which means the lowest point does not exist since neg infinity isn't a number :p
thank you both of you.. that clears that I think. yes the interval is undefined, so I would think range is infinite
and thanks for a prompt response..

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