Basic Analysis I — Real Analysis · Problem 4.2.8

The Derivative — Jiri Lebl

Mathematics — Real Analysis · equal-derivatives-differ-by-constant

Problem

Suppose

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

and

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

are differentiable functions such that

f'(x) = g'(x)

for all

x \in (a,b)

, then show that there exists a constant

C

such that

f(x) = g(x) + C