Definition

1. Noun (plural of ):
   • The highest or greatest possible amount, degree, or value: "maxima" refers to the plural form of "maximum," indicating multiple instances of the highest point or peak in a set of data, values, or measurements.
   • In mathematics: The largest value of a function within a given range or on a specific interval; a point at which a function reaches its greatest value locally or globally.

Usage Examples

• General context:

  • The temperature maxima for the week were recorded on Tuesday and Friday. (The highest temperatures occurred on those two days.)
  • Economists study the maxima and minima of market trends to predict fluctuations. (The highest and lowest points of economic data.)

• Mathematical context:

  • The function has two local maxima at x = 2 and x = 5. (The function reaches peak values at those points, but not necessarily the overall highest value.)
  • Finding the maxima of a curve helps determine optimal conditions in engineering. (Identifying the peak points of a mathematical graph.)

Advanced Usage

• "local maxima": In calculus, a point where a function has a value greater than all nearby points but not necessarily the absolute highest value overall.

  • The graph shows several local maxima, but only one global maximum. (Peaks in specific intervals versus the overall peak.)

• "global maxima": The absolute highest value of a function across its entire domain.

  • The algorithm seeks the global maxima of the profit function. (The single highest profit point.)

Variants and Related Words

• Maximum (noun, singular): The highest point or value.

  • The maximum temperature today is 30°C. (The single highest temperature.)

• Maximal (adjective): Relating to or being a maximum; as great as possible.

  • The maximal effort was required to complete the project. (The greatest possible effort.)

• Maximize (verb): To make as large or great as possible.

  • We need to maximize our resources. (Use resources to their fullest extent.)

Synonyms

• Peaks: The highest points of a set or function.
  • The peaks of the mountain range are similar to the maxima of a graph.
• Highs: Informal term for highest values.
  • Stock market highs and lows are like maxima and minima.
• Culminations: The highest or climactic points of something.
  • The culminations of the festival were the fireworks displays.

Related Idioms

• "Reach a maximum": To attain the highest possible level.

  • The noise level reached a maximum during the concert. (The loudest point.)

• "At its peak": At the highest point of activity, development, or value.

  • The athlete was at his peak during the Olympics. (At his maximum performance.)

Note: "Maxima" is exclusively a plural noun. It does not have phrasal verbs or idioms of its own, but it is commonly used in technical and formal contexts.