Basic Analysis I — Real Analysis · Problem 3.2.11

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · continuous-functions

Problem

Let f:R→Rf : \mathbb{R} \to \mathbb{R} be continuous. Suppose f(c)>0f(c) > 0. Show that there exists an α>0\alpha > 0 such that for all x∈(c−α,c+α)x \in (c - \alpha, c + \alpha), we have f(x)>0f(x) > 0.

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