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anonymous

  • one year ago

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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  1. Rizags
    • one year ago
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    whats the function?

  2. anonymous
    • one year ago
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    1 sec

  3. myininaya
    • one year ago
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    |dw:1434750076795:dw| something like this?

  4. anonymous
    • one year ago
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    I think so yes..

  5. anonymous
    • one year ago
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    \[-577 + 736 x - 324 x^2 + 60 x^3 - 4 x^4\]

  6. myininaya
    • one year ago
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    well it doesn't have a absolute min

  7. myininaya
    • one year ago
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    you are looking at a polynomial ?

  8. myininaya
    • one year ago
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    polynomials don't have vertical asymptotes

  9. myininaya
    • one year ago
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    I guess you are talking about the end behavior of the graph maybe

  10. myininaya
    • one year ago
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    when you talk about going to negative infinity ?

  11. myininaya
    • one year ago
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    anyways to find the lowest point I would first differentiate your polynomial there if I were you

  12. myininaya
    • one year ago
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    then find critical numbers by finding when f'=0

  13. anonymous
    • one year ago
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    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?

  14. myininaya
    • one year ago
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    are you looking for local min?

  15. myininaya
    • one year ago
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    or absolute min?

  16. myininaya
    • one year ago
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    as you said there is no absolute min because the end behavior of the graph goes to neg infinity

  17. anonymous
    • one year ago
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    That might be my answer then...

  18. myininaya
    • one year ago
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    is there an interval for which you are to restrict this function to?

  19. anonymous
    • one year ago
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    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..

  20. anonymous
    • one year ago
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    something I should have remembered from high school I guess.. but then couldnt find even anything on google that answered that directly.

  21. myininaya
    • one year ago
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    well I think lowest point is absolute min

  22. myininaya
    • one year ago
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    but there are lowest points on smaller intervals of the graph

  23. dan815
    • one year ago
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    the lowest point is the lowest point on the graph, which is negative infinity :)

  24. myininaya
    • one year ago
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    @dan815 which means the lowest point does not exist since neg infinity isn't a number :p

  25. anonymous
    • one year ago
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    thank you both of you.. that clears that I think. yes the interval is undefined, so I would think range is infinite

  26. anonymous
    • one year ago
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    and thanks for a prompt response..

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