power function
Theorem.
The power function is differentiable with the derivative and strictly increasing if and strictly decreasing if (and 1 if ).
The power functions comprise the natural power functions with , the root functions with and other fraction power functions with any fractional number.
Note. The power may of course be meaningful also for other than positive values of , if is an integer. On the other hand, e.g. has no real values — see the general power.
Title | power function |
Canonical name | PowerFunction |
Date of creation | 2013-03-22 14:46:32 |
Last modified on | 2013-03-22 14:46:32 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 17 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 26A99 |
Related topic | PropertiesOfTheExponential |
Related topic | FractionPower |
Related topic | CubeOfANumber |
Related topic | Polytrope |
Related topic | PowerTowerSequence |
Related topic | LaplaceTransformOfLogarithm |
Defines | natural power function |
Defines | root function |
Defines | fraction power function |