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Thread: vertical and horizontal asymptote for curve sketching

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    vertical and horizontal asymptote for curve sketching

    If f(x) graph has a vertical or horizontal asymptote will the derivative graph have an exact vertical or horizontal asymptote in the same place when curve sketching?

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  2. #2
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    Quote Originally Posted by happy8588 View Post
    If f(x) graph has a vertical or horizontal asymptote will the derivative graph have an exact vertical or horizontal asymptote in the same place when curve sketching?

    Thanks
    vertical asymptote ... I would venture to say yes.
    ... (now watch one of MHF's more knowledgeable individuals provide a counterexample ... I can't think of one.)

    horizontal asymptote(s), don't think so ... consider the graph of f(x) = arctan(x) and the graph of its derivative.
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