Vipul: Created page with "==Definition== The '''square function''' or '''square map''' is a function defined on all real numbers that sends any real number to its square, i.e., its product with itself. ..."

2011-08-26T10:48:29Z

Created page with "==Definition== The '''square function''' or '''square map''' is a function defined on all real numbers that sends any real number to its square, i.e., its product with itself. ..."

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==Definition==

The '''square function''' or '''square map''' is a function defined on all real numbers that sends any real number to its square, i.e., its product with itself.

==Key data==

{| class="sortable" border="1"
! Item !! Value
|-
| default [[domain]] || all real numbers, i.e., all of <math>\R</math>
|-
| [[range]] || all nonnegative real numbers, i.e., <math>[0,\infty)</math>, same as <math>\{ y \mid y \ge 0 \}</math><br>no absolute maximum value; [[absolute minimum value]]: 0
|-
| [[local maximum value]]s and points of attainment || no local maximum value
|-
| [[local minimum value]]s and points of attainment || local minimum value of 0 attained at 0
|-
| [[points of inflection|point of inflection]] (both coordinates) || no points of inflection
|-
| [[derivative]] || <math>x \mapsto 2x</math>
|-
| [[second derivative]] || <math>x \mapsto 2</math>
|-
| [[antiderivative]] || <math>x \mapsto \frac{x^3}{3} + C</math>
|-
| interval description based on increase/decrease and concave up/down || <math>(-\infty,0)</math>: decreasing and concave up<br><math>(0,\infty)</math>: increasing and concave up
|}

Square function - Revision history

Vipul: Created page with "==Definition== The '''square function''' or '''square map''' is a function defined on all real numbers that sends any real number to its square, i.e., its product with itself. ..."