# Secant line in Fermat's Theorem

by Bipolarity
Tags: fermat, line, secant, theorem
 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 $$\lim_{x→c}\frac{f(x)-f(c)}{x-c} > 0$$ then there exists an open interval (a,b) containing c such that $$\frac{f(x)-f(c)}{x-c} > 0$$ for all c in that interval. How does this follow from the definition of the derivative? I appreciate all help. Thanks!
 HW Helper Thanks PF Gold P: 7,226 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.

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