Vipul: /* Key data */

2011-12-13T17:45:05Z

Key data

← Older revision		Revision as of 17:45, 13 December 2011
Line 36:		Line 36:
	\| intervals of increase/decrease and concave up/down \|\| increasing and concave down on <math>(-\infty,0)</math>.<br>increasing and concave up on <math>(0,\infty)</math>.		\| intervals of increase/decrease and concave up/down \|\| increasing and concave down on <math>(-\infty,0)</math>.<br>increasing and concave up on <math>(0,\infty)</math>.
	\|}		\|}

			==Graph==

			Below is the graph of the function, with domain restricted to <math>[-1,1]</math>:

			[[File:Cubefunctionbasic.png\|600px]]

			Below is the graph of the function and its derivative, with domain restricted to <math>[-1,1]</math>:

			[[File:Cubefunctionwithderivative.png\|600px]]

Vipul: Created page with "{{particular function}} ==Definition== This function, termed the '''cube function''' or '''cubing function''' or '''cube map''', is the function that sends any element to its c..."

2011-09-04T22:18:32Z

Created page with "{{particular function}} ==Definition== This function, termed the '''cube function''' or '''cubing function''' or '''cube map''', is the function that sends any element to its c..."

New page

{{particular function}}

==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:

<math>\! x \mapsto x^3 = xxx</math>

==Key data==

{| class="sortable" border="1"
! Item !! Value
|-
| default [[domain]] || all [[real number]]s, i.e., all of <math>\R</math>
|-
| [[range]] || all [[real number]]s
|-
| [[period]] || not a periodic function
|-
| [[inverse function]] || [[cube root function]] (both the cube function and the cube root function are [[one-one function]]s)
|-
| [[first derivative]] || <math>x \mapsto 3x^2</math>, i.e., thrice the [[square function]]
|-
| [[second derivative]] || <math>x \mapsto 6x</math>, i.e., six times the [[identity function]]
|-
| [[antiderivative]] || <math>x \mapsto x^4/4</math>, i.e., <math>1/4</math> times the [[fourth power function]]
|-
| important symmetries || the origin <math>(0,0)</math> is a point of half turn symmetry
|-
| [[local minimum value]]s and points of attainment || there are no local minimum values because the function is increasing throughout its domain
|-
| [[local maximum value]]s and points of attainment || there are no local maximum values because the function is increasing throughout its domain
|-
| [[point of inflection|points of inflection]] (both coordinates) || the origin <math>(0,0)</math>
|-
| intervals of increase/decrease and concave up/down || increasing and concave down on <math>(-\infty,0)</math>.<br>increasing and concave up on <math>(0,\infty)</math>.
|}

Cube function - Revision history

Vipul: /* Key data */

Vipul: Created page with "{{particular function}} ==Definition== This function, termed the '''cube function''' or '''cubing function''' or '''cube map''', is the function that sends any element to its c..."