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.(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Secant line in Fermat's Theorem

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