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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- Nov 16th 2010, 05:25 PMhappy8588vertical 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?

Thanks - Nov 16th 2010, 05:35 PMskeeter
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.