Basic Analysis I — Real Analysis · Problem 3.6.7

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · monotone-functions-continuity

Problem

Let

I \subset \mathbb{R}

be an interval and

f : I \to \mathbb{R}

a function. Suppose that for each

c \in I

, there exist

a, b \in \mathbb{R}

with

a > 0

such that

f(x) \geq ax + b

for all

x \in I

and

f(c) = ac + b

. Show that

f

is strictly increasing.