Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Secant line in Fermat's Theorem

  1. Mar 8, 2012 #1
    I'm trying to understand something in Fermat's Theorem. I can't really phrase it in words, but I will write what my textbook says.

    Apparently if

    [tex] \lim_{x→c}\frac{f(x)-f(c)}{x-c} > 0 [/tex]

    then there exists an open interval (a,b) containing c such that

    [tex] \frac{f(x)-f(c)}{x-c} > 0 [/tex] for all c in that interval.

    How does this follow from the definition of the derivative?

    I appreciate all help.

    Thanks!
     
  2. jcsd
  3. Mar 8, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    That is a general property of limits. If$$
    \lim_{x\rightarrow c}g(x) = L > 0$$then there is an open interval ##I## containing ##c## on which ##g(x)>0##. It comes directly from the ##\epsilon - \delta## definition of limit.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Secant line in Fermat's Theorem
  1. Secant series (Replies: 2)

Loading...