Concavity: meaning, definitions and examples
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concavity
[ kənˈkævəti ]
mathematics, geometry
Concavity refers to the property of a curve or a function that describes its direction of bending. A curve is considered concave if it bends towards its interior, while a function is concave if the line segment between any two points on the graph lies below the graph itself. This concept plays a significant role in calculus, particularly when analyzing the second derivative of a function. Understanding concavity helps in determining the behavior of functions, including identifying local maxima and minima.
Synonyms
Examples of usage
- The concavity of the function indicates whether it is increasing or decreasing.
- In geometry, we often discuss the concavity of various shapes.
- The concavity of the demand curve can affect pricing strategy.
Translations
Translations of the word "concavity" in other languages:
🇵🇹 concavidade
🇮🇳 उल्टी आंतरिकता
🇩🇪 Konkavität
🇮🇩 konkavitas
🇺🇦 увігнутість
🇵🇱 wklęsłość
🇯🇵 凹凸
🇫🇷 concavité
🇪🇸 concavidad
🇹🇷 çökmüşlük
🇰🇷 오목함
🇸🇦 تجويف
🇨🇿 konkávnost
🇸🇰 konkávnosť
🇨🇳 凹性
🇸🇮 konkavnost
🇮🇸 kúrvun
🇰🇿 құлақшақтық
🇬🇪 კონკავობა
🇦🇿 konkavlıq
🇲🇽 concavidad
Etymology
The term 'concavity' comes from the Latin root 'concavus,' which means 'hollow or curved inward.' This root itself is derived from 'con-' (with) and 'cavus' (hollow), suggesting the idea of being inwardly curved. The use of 'concavity' in mathematics dates back to the development of early geometry, where mathematicians sought to describe the shape and bending of curves. Over centuries, the concept was refined and formalized in calculus, where it became essential to understanding the behavior of functions and their derivatives. Today, 'concavity' is a fundamental concept in various fields including economics, physics, and engineering, influencing models and theories in those disciplines.