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- A function is concave (convex) if the graph of the function is always above (below) any chord (line segment between two points in the graph).
pareto.uab.cat/xvila/Micro_I/ConcavityConvexityQuasiconcaviyQuasiconvexity.pdfNotes on Concavity, Convexity, Quasiconcavity and Quasiconvexity
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Sep 9, 2023 · Definition: An object or a function is concave if it curves inward. In simple terms, it’s hollow or bowed in, much like a cave. Everyday Examples: A bowl. A satellite dish. A spoon’s interior. Skateboard ramps. A pie with a slice taken out of it. Convex.
In a ray diagram, a concave lens is drawn as a vertical line with inward facing arrows to indicate the shape of the lens. Learn about and revise lenses, images,...
A function $f(x)$ is said to be quasi-concave if its domain and all its $\alpha$-superlevel sets defined as $$\mathcal{S}_\alpha \triangleq\{x|x\in dom f, f(x)\geq\alpha\}$$ are convex for every $\alpha$.
Definition: Concavity and Inflection. From the diagrams, we can see that 𝑓 (𝑥) = 𝑥 is a good example of a function that is concave upward over its entire domain; it curves upward and the value of its slope is increasing over its entire domain.
It is also possible to characterize concavity or convexity of functions in terms of the convexity of particular sets. Given the graph of a function, the hypograph of f,
An ordinal as well as a cardinal utility function can be concave. Concavity, which is standardly derived from the fact that preferences are convex, is a property of utility functions seemingly independent from ordinal or cardinal assumptions.
