Inverse Functions and Differentiation - Additional Properties

Additional Properties

  • Integrating this relationship gives
This is only useful if the integral exists. In particular we need to be non-zero across the range of integration.
It follows that a function that has a continuous derivative has an inverse in a neighbourhood of every point where the derivative is non-zero. This need not be true if the derivative is not continuous.

Read more about this topic:  Inverse Functions And Differentiation

Famous quotes containing the words additional and/or properties:

    Don’t you think I’ve had enough excitement for one evening, without the additional thrill of a strange man making love to me?
    John L. Balderston (1899–1954)

    A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.
    Ralph Waldo Emerson (1803–1882)