Register to reply

Secant line in Fermat's Theorem

by Bipolarity
Tags: fermat, line, secant, theorem
Share this thread:
Bipolarity
#1
Mar8-12, 12:07 PM
P: 783
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!
Phys.Org News Partner Science news on Phys.org
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker
LCKurtz
#2
Mar8-12, 02:00 PM
HW Helper
Thanks
PF Gold
LCKurtz's Avatar
P: 7,661
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.


Register to reply

Related Discussions
Fermat's last theorem General Math 5
Fermat's little theorem Calculus & Beyond Homework 6
Fermat's theorem Linear & Abstract Algebra 0
Equation of secant line Precalculus Mathematics Homework 6
Fermat's Last Theorem (FLT) Linear & Abstract Algebra 10