CALCULUS Understanding Its Concepts and Methods

Rates of change

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

If the variable
*y*
changes from
*y*_{0}
to
*y*_{1}
as the variable
*x*
changes from
*x*_{0}
to
*x*_{1} ,
then the rate of change of
*y*
with respect to
*x*
is the
ratiowhich
is the slope of the line joining the two points
(*x*_{0},*y*_{0})
and
(*x*_{1},*y*_{1}) .

The average rate of change of a function
*f*
over the interval
*a ≤ x ≤ b*
is the
slopeof
the line joining the two points
(*a*,*f*(*a*))
and
(*b*,*f*(*b*)).

The
instantaneous rate of change of a function
*f*
at
*a*
is

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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.