- #1
Bipolarity
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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!
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!