difference quotient

The difference quotient

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

of a complex (http://planetmath.org/ComplexFunction) or real function $f$ 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 $f$ the difference quotient may be interpreted as the slope of a secant line of the graph of the function.

Title	difference quotient
Canonical name	DifferenceQuotient
Date of creation	2013-03-22 17:30:46
Last modified on	2013-03-22 17:30:46
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	4
Author	pahio (2872)
Entry type	Definition
Classification	msc 26A06
Classification	msc 30A99
Related topic	Derivative2
Related topic	Slope
Related topic	SecondDerivativeAsSimpleLimit