Convexity and Concavity

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a property of the graph of the function y = f(x) (a curve) that consists in the fact that each arc of the curve lies neither higher nor lower than its chord. In the first instance the graph of the function f(x) is convex downward (concave upward) and the function itself is called convex; in the second instance the graph is concave downward (convex upward) and the function is called concave. If there are derivatives f′(x) and f′(x), then the first instance applies when f′(x)= >̳ 0 and the second when f′(x) <̳ 0 (at all points along the interval under consideration). Convexity downward can also be characterized by the fact that the arc of the curve lies no lower than the tangent at any of its points, and concavity downward by the fact that the arc of the curve lies no higher than the tangent. Convexity and concavity of a surface are defined analogously.

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No references found			Convexity and concavity lie at the crux of What if the Phone Rings, 2003, the artist's lumpen version of the Three Graces realized as lit candles that melt over the course of their display. Taste tests by Kuo, Michelle / Artforum International In particular, the present analysis, for the first time, has shown that convexity and concavity of the demand curves may have different implications on the output effect of price discrimination. Adjusted concavity and the output effect under monopolistic price ... by Xinghe Wang / Southern Economic Journal			Converter Substation Converter Tube Converter, Single-Armature Convertibility of Currencies convertible convertiplane convex convex angle Convex Area on a Plane Convex Body convex combination Convex Computer Corporation convex curve convex function convex function in the sense of Jensen convex hull convex linear combination convex linear hull convex polygon convex polyhedron convex polytope convex programming convex sequence convex set convex span Convexity and Concavity convexo-concave conveyance Conveyer Assembly conveying hose Conveyor Conveyor Belt conveyor belt balance Conveyor Bridge convict convict labor Convicted Person Conviction, Record of convivium convocation Convocation Sejm convolute convolute bedding Convolution convolution family convolution rule convolution theorem convolutional code convolver Convolvulaceae convolvulus			convex polyhedron Convex polytope Convex programming Convex region Convex regular polyhedron Convex regular polyhedron convex sequence Convex set convex shape convex sole convex sole convex sole convex sole Convex span convex spherical lens Convex subset Convex/Concave Index Convexed Convexed Convexed Convexed Convexedly Convexedness convexities convexities convexity convexity convexity convexity Convexity (mathematics) Convexity and Concavity convexity meningiomas convexity meningiomas convexity meningiomas convexly convexly convexly convexly convexness convexo-concave convexo-concave convexo-concave convexo-concave lens convexo-convex convexo-convex convexo-convex lens Convexo-plane convexoconcave convexoconcave lens convexoconcave lens convexoconcave lens convexoconvex convey convey convey convey convey a meaning convey a verbal image convey an impression of convey away convey by deed

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