Definition:Difference Quotient

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Let $V$ be a vector space over the real numbers $\R$.

Let $f: \R \to V$ be a function.

A difference quotient is an expression of the form:

$\dfrac {\map f {x + h} - \map f x} h$

where $h \ne 0$ is a real number.

Geometric Interpretation

The difference quotient is the slope of the secant line of the graph of $f$ connecting points $P_1 = \tuple {x, \map f x}$ and $P_2 = \tuple {x + h, \map f {x + h} }$.

Also known as

A difference quotient is also known as a Newton quotient, for Isaac Newton

Also see