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.