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Rates of change

A rate of change is the ratio of changes in two variables.

If the variable y changes from y0  to y1 as the variable x changes from x0  to x1 , then the rate of change of y with respect to x is the ratioMATHwhich is the slope of the line joining the two points (x0,y0)  and (x1,y1) .

The average rate of change of a function f over the interval a ≤ x ≤ b  is the slopeMATHof the line joining the two points (a,f(a))  and  (b,f(b)).
averageroc.png
The instantaneous rate of change of a function f at a isMATH


A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


Difference quotient

Slope


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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