Concave Function

A Concave Function is a convex function upside down.

See: Convex Function, Convex Set.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Concave_function
  • QUOTE: In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex(...) A function [math]\displaystyle{ f }[/math] is concave over a convex set if and only if the function [math]\displaystyle{ −f }[/math] is a convex function over the set.

1999

• (Wolfram Mathworld , 1999) ⇒ http://mathworld.wolfram.com/ConcaveFunction.html
  • QUOTE: A function [math]\displaystyle{ f(x) }[/math] is said to be concave on an interval [math]\displaystyle{ [a,b] }[/math] if, for any points [math]\displaystyle{ x_1 }[/math] and [math]\displaystyle{ x_2 }[/math]in </math>[a,b]</math> the function [math]\displaystyle{ -f(x) }[/math] is convex on that interval.

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