Math

Technology in Mathematics Education

Fall 2008, Volume 9, Issue 1

**Difference Quotients**

Typically in Calc I, the forward difference is used, but in numerical work usually the centered difference is used. Having students try all three with limits or numerical calculations can serve to enhance their understanding of derivatives.

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Editor: Scott S Albert

Meditating Mathematicians

M^{2}

Critical Thinking in Mathematics Education

Consider:

and

then

plotting increment same as step size

Observations:

1)

The forward and backward difference approximations match the analytical solution exactly at only one point over the range plotted above.

2)

The centered difference method never exactly matches the analytical solution over the range of values plotted but, except in the region of the points where the FD and BD procedures match exactly, is much closer to the analytical derivative.