Lebl-Basic-Analysis-I · Problem 4.2.8

The Derivative

Mathematics · mean-value-theorem-functions-differ-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