Talk:First derivative test

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Why is it necessery that ' f' has to be continuous '? If f differentiable at every poitn of an interval, then f' is Darboux continuous. Hence, if f'|_{(x-r,x)}>0\, and f'|_{(x,x+r)}<0\, (notations as in the article), then f' has to be zero at some point and this point can only be x. Mozó (talk) 08:12, 19 November 2007 (UTC)