1. The problem statement, all variables and given/known data Let [tex]h: \Re \rightarrow \Re[/tex] be a continuous function such that h(a)>0 for some [tex]a \in \Re[/tex]. Prove that there exists a [tex] \delta >0 [/tex] such that h(x)>0 provided that [tex] |x-a|< \delta [/tex]. 2. Relevant equations Continuity of h means that there exists and [tex]\epsilon >0 [/tex] such that [tex] |h(x)-h(a)| < \epsilon [/tex] provided that [tex] |x-a| < \delta [/tex] 3. The attempt at a solution I tried starting with the definition of continuity and perhaps the intermediate value theorem, but I haven't been able to get started. Any suggestions on how to get started? Thanks!