PlanetMath: difference quotient

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difference quotient

(Definition)

The difference quotient

$\displaystyle \frac{f(z+\Delta{z})-f(z)}{\Delta{z}}$

of a complex or real function

is the ratio of the change of the function to the corresponding change of the variable.

The difference quotient is needed in defining the derivative of the function. In the case of a real function the difference quotient may be interpreted as the slope of a secant line of the graph of the function.

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"difference quotient" is owned by pahio.

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See Also: derivative, slope

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Cross-references: graph, secant line, slope, derivative, variable, function, ratio, real function
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This is version 1 of difference quotient, born on 2007-08-29.
Object id is 9903, canonical name is DifferenceQuotient.
Accessed 2197 times total.

Classification:

AMS MSC:	26A06 (Real functions :: Functions of one variable :: One-variable calculus)
	30A99 (Functions of a complex variable :: General properties :: Miscellaneous)

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