Square function

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

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