Basic Analysis I — Real Analysis · Problem 4.2.6

The Derivative — Jiri Lebl

Mathematics — Real Analysis · strictly-increasing-positive-derivative

Problem

Finish the proof of Proposition 4.2.8. That is, suppose

I

is an interval and

f : I \to \mathbb{R}

is a differentiable function such that

f'(x) > 0

for all

x \in I

. Show that

f

is strictly increasing.