1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Smoothness of functions

  1. Aug 16, 2007 #1
    If [tex] f \cdot f [/tex] and [tex] f \cdot f \cdot f [/tex] is smooth, does it follow that [tex] f [/tex] is smooth?

    So does [tex] f \cdot f \in C^{\infty} \ \text{and} \ f \cdot f \cdot f \in C^{\infty} \Rightarrow f \in C^{\infty} [/tex]?

    Maybe we could generalize a bit more: Given that [tex] f^{n} , f^{n-1} \in C^{\infty} [/tex] does it follow that [tex] f \in C^{\infty} [/tex] (where [tex] f^n [/tex] is the function raised to some power [tex] n [/tex])?
    Last edited: Aug 16, 2007
  2. jcsd
  3. Aug 16, 2007 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Well, what does dividing tell you?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook