Let \(D\subseteq\mathbb R\) (\(D\) is a subset of real numbers) and let \(f:D\to\mathbb R\) be a function. Let \(b,a\in D\), \(b\neq a\). The difference quotient of \(f\) is the function \(\Delta f(b,a):D\times D\to \mathbb R\), defined by
\[\Delta f(b,a):=\frac {f(b)-f(a)}{b-a},\quad b\neq a.\]
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