Let I (a, b) and f I R We say that f is ' 'locally increasing ' ' at c I if there exists 0 such that f is increasing on I (c (c), c (c)) Prove that if f is locally increasing at every point of I, then f is increasing on I ...

The hypothesis that f is locally increasing presents us with a gauge If x i 1 x i ...

Let I := (a, b) and f : I R. We say that f is ''locally

Question:

Let I := (a, b) and f : I → R. We say that f is ''locally increasing'' at c ∈ I if there exists δ© > 0 such that f is increasing on I ∩ (c - δ(c), c + δ(c)). Prove that if f is locally increasing at every point of I, then f is increasing on I.