# Math Help - vertical and horizontal asymptote for curve sketching

1. ## 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?

Thanks

2. Originally Posted by happy8588
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.