Editing Rate (mathematics) (section)

==Rate of change{{anchor|Of change}}==
Consider the case where the numerator <math>f</math> of a rate is a function <math>f(a)</math> where <math>a</math> happens to be the denominator of the rate <math>\delta f/\delta a</math>. A rate of change of <math>f</math> with respect to <math>a</math> (where <math>a</math> is incremented by <math>h</math>) can be formally defined in two ways:<ref>{{cite book|last1=Adams |first1=Robert A. |title=Calculus: A Complete Course |edition=3rd |year=1995 |publisher=Addison-Wesley Publishers Ltd. |isbn=0-201-82823-5 |page=129}}</ref>
: <math>
\begin{align}
\mbox{Average rate of change} &= \frac{f(x + h) - f(x)}{h}\\
\mbox{Instantaneous rate of change} &= \lim_{h \to 0}\frac{f(x + h) - f(x)}{h}
\end{align}
</math>
where ''f''(''x'') is the function with respect to ''x'' over the interval from ''a'' to ''a''+''h''. An instantaneous rate of change is equivalent to a [[derivative]].

For example, the average [[speed]] of a car can be calculated using the total distance traveled between two points, divided by the travel time. In contrast, the instantaneous velocity can be determined by viewing a [[speedometer]].