# 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 |