Constant Difference Theorem

analysis

Definition

Constant Difference Theorem

If two functions have identical derivatives over an interval, they differ only by a constant value.

Let $f$ and $g$ be two functions that are continuous on an interval $[a,b]$ and differentiable on $(a,b)$:

$$\forall x\in (a,b):f^{\prime }(x)=g^{\prime }(x)⟹\exists C\in \mathbb{R}:f(x)=g(x)+C$$