If f is differentiable on [a,b] and f'(c)>0 for some a<c<b then does this imply that f is monotonically increasing on some neighborhood of c? My intuition says yes but I just can't figure out a way to prove it. (not homework). Because of the weierstrass function I'm pretty sure differentiability on the whole neighborhood has to be utilized in some way..(adsbygoogle = window.adsbygoogle || []).push({});

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# Differentiable on interval implies monotonic on some neighborhood of every point

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