Difference quotient/D in R/Definition

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

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

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

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

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