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concavity

concavity

9.3
A graph that curves downward so every straight line between two points stays below it
  • noun
  • /kɒnˈkævɪti/
  • Specialized
translation icon : concavidad
  • To determine the concavity of the function, we analyze the second derivative of its graph.
  • concavity violations

Examples

  • Given the concavity of the revenue function R(Q), the optimal condition is:

    Academic text (1990)
  • The above equation holds because of the concavity of the cost function and the constraints.

    Academic text (1997)
  • These are places where the concavity might change.

  • It's the same thing as getting concavity of the expenditure function.

  • And then to find the concavity, we take the derivative of DYDX.

  • Concavity violations were not found in most cases for the properties of the translog cost function.

    Academic text (1993)
  • However, the estimation results of the present study indicate no violation of concavity and monotonicity for all sectors studied.

    Academic text (1993)
  • The use of the translog form in the energy cost function sometimes violates consistency in economic theories, such as concavity and monotonicity.

    Academic text (1993)
  • However, considering the appropriate results of concavity and the significance of the elasticity estimates, aggregates of oil and gas were assumed for every sector in the study.

    Academic text (1993)
  • Projective geometry, minimal surfaces, elliptical orbits, and concavity are some of the mathematical concepts conveyed in a hands-on fashion.

    Academic text (2001)

Antonyms

convexity
  • Specialized
1 7.6

A surface that curves or bulges outward like the outside of a ball

Surface Forms

concavity singular
concavities plural

Morphology

concavity = concave (transparent) = concave + ity

Mathematical 'concavity' is a technical extension of 'concave' describing the property of a graph; formation is the regular adjective-to-noun nominalization.

Etymology

The word concavity comes from Latin con- and cavus meaning 'hollow', the same root in cave and cavity. In math that 'hollow' picture helps: a concave curve bends inward like a bowl, which is why it has one clear highest point and is easier to find the top value.