Cube function

This article is about a particular function from a subset of the real numbers to the real numbers. Information about the function, including its domain, range, and key data relating to graphing, differentiation, and integration, is presented in the article.
View a complete list of particular functions on this wiki

Definition

This function, termed the cube function or cubing function or cube map, is the function that sends any element to its cube, i.e., to its third power. It is defined as:

$x\mapsto x^3=xxx$

Key data

Item	Value
default domain	all real numbers, i.e., all of $\mathbb{R}$
range	all real numbers
period	not a periodic function
inverse function	cube root function (both the cube function and the cube root function are one-one functions)
first derivative	$x\mapsto 3x^2$, i.e., thrice the square function
second derivative	$x\mapsto 6x$, i.e., six times the identity function
antiderivative	$x\mapsto x^4/4$, i.e., $1/4$ times the fourth power function
important symmetries	the origin $(0,0)$ is a point of half turn symmetry
local minimum values and points of attainment	there are no local minimum values because the function is increasing throughout its domain
local maximum values and points of attainment	there are no local maximum values because the function is increasing throughout its domain
points of inflection (both coordinates)	the origin $(0,0)$
intervals of increase/decrease and concave up/down	increasing and concave down on $(-\mathrm{\infty },0)$. increasing and concave up on $(0,\mathrm{\infty })$.