CALCULUS Understanding Its Concepts and Methods

Difference quotient,Symmetric difference quotient,Approximate derivative

The difference quotient** **of
*f*
at
*a*
is the
quotient

The difference quotient is an approximation to the derivative
*f'*(*a*) .

The symmetric difference
quotient** **of
*f*
at
*a* is the
quotient

The symmetric difference quotient is the average of the difference quotients
for positive and negative values of
*h*.
It is usually a much better approximation to the derivative
*f ' *(*a*)
than the one-sided difference quotients.

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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.