Property of a continuous function in the neighborhood of a point – math.stackexchange.com

Property of a continuous function in the neighborhood of a point – math.stackexchange.com

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Let $f:\mathbb{R} \to \mathbb{R}$ be a differentiable function. Let $a \in \mathbb{R}$ and define the following sets: \begin{align*} M= \{x>a \mid f(t)>f(a), \forall t \in (a,x] \}\\ ...

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