Difference quotient/D in R/Definition

Difference quotient

Let ${}D\subseteq \mathbb {R}$ be a subset, ${}a\in D$ a point, and

$f\colon D\longrightarrow \mathbb {R}$

a function. For ${}x\in D$, ${}x\neq a$, the number

${\frac {f(x)-f(a)}{x-a}}$

is called the difference quotient of ${}f$ for ${}a$ and ${}x$.