Basic Analysis I — Real Analysis · Problem 4.2.7

The Derivative — Jiri Lebl

Mathematics — Real Analysis · nonzero-derivative-sign

Problem

Suppose

f : (a,b) \to \mathbb{R}

is a differentiable function such that

f'(x) \neq 0

for all

x \in (a,b)

. Suppose there exists a point

c \in (a,b)

such that

f'(c) > 0

. Prove

f'(x) > 0

for all

x \in (a,b)