What is Convex function?
[[Image:ConvexFunction.svg|thumb|300px|right|Convex function on an interval.]] [[Image:Epigraph convex.svg|right|thumb|300px|A function (in black) is convex if and only if the region above its [[graph]] (in green) is a [[convex set]].]] In [[mathematics]], a '''convex function''' is any [[function (mathematics)|function]] with value of the [[weighted average]] of 2 points is [[less than or equal to]] the weighted average of the function at those points. Also, a function is convex [[if and only if]] its [[epigraph (mathematics)|epigraph]] is a [[convex set]]. == Examples == Three examples are: * A [[line]]: <math>f(x) = x</math> * A [[parabola]]: <math>f(x) = x^2</math> * [[Absolute value]]: <math>f(x) = |x|</math> {{Math-stub}} [[Category:Functions and mappings]]