Definition:Difference Quotient

Definition
Let $V$ be a vector space over $\R$.

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

A difference quotient is an expression of the form:
 * $\displaystyle \frac { f\left({x + h}\right) - f\left({x}\right) } {h}$

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 $P_1 = \left({x,f\left({x}\right)}\right)$ and $P_2 = \left({x+h,f\left({x+h}\right)}\right)$.

Also see

 * Definition:Finite Difference Operator
 * Definition:Left Difference Quotient
 * Definition:Right Difference Quotient
 * Definition:Derivative