concave function
[/kɑnˈkeɪv ˈfʌŋkʃən/]
nounfemininepl: concave functions / funções côncavas
função côncava
1. A mathematical function where the line segment connecting any two points on its graph lies below or on the graph itself; a function f where f(λx + (1-λ)y) ≥ λf(x) + (1-λ)f(y) for all x, y in the domain and λ ∈ [0,1]
The logarithmic function is a concave function on the positive real numbers.
A função logarítmica é uma função côncava nos números reais positivos.
2. In economics and optimization, a function whose graph curves downward, often representing utility, production output, or diminishing returns
The utility function in consumer theory is typically assumed to be a concave function to model diminishing marginal utility.
A função de utilidade na teoria do consumidor é tipicamente assumida como uma função côncava para modelar a utilidade marginal decrescente.
This is a technical mathematical and economic term used primarily in academic and professional contexts in both Brazil and the USA. It is fundamental to microeconomic theory, optimization problems, and mathematical analysis. The term is identical in Portuguese and English academic usage, reflecting the universal nature of mathematical terminology.
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