# difference quotient

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

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 DifferenceQuotient 2013-03-22 17:30:46 2013-03-22 17:30:46 pahio (2872) pahio (2872) 4 pahio (2872) Definition msc 26A06 msc 30A99 Derivative2 Slope SecondDerivativeAsSimpleLimit