I've been thinking... Since derivatives can be written as:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f'(c)= \lim_{x\rightarrow{c}}\frac{f(x)-f(c)}{x-c}[/tex]

and for the limit to exist, it's one sided limits must exist also right?

So if the one sided limits exist, and thus the limit as x approaches c (therefore the derivative at c) (but f(x) is not continuous at c) why can't f(x) have a derivative at c?

I'm just looking at it from that standpoint (I know that derivatives are basically the rate of change of a function at a point or in general).

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# Homework Help: Why does differentiability imply continuity?

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