I am trying to find a counter example to falsify the following statement:
"if $f$ is differentiable at $a$ and $f'(a)>0$, then $f(a)$ is increasing in a neighbourhood of $a$"
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See Here http://math.stackexchange.com/questions/1499789/how-to-prove-fa0-means-f-is-increasing/1500182#1500182 – Kelenner Dec 22 '15 at 17:49
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Thank you! So is it true that on any closed interval for which $f'(a)$ is positive this statement will be true? – john melon Dec 22 '15 at 18:34
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Sure, that follows from the mean value theorem. – zhw. Dec 22 '15 at 20:54