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:
“The world will never be long without some good reason to hate the unhappy; their real faults are immediately detected, and if those are not sufficient to sink them into infamy, an additional weight of calumny will be superadded.”
—Samuel Johnson (1709–1784)
“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)