extremum
Maximum or minimum
An extremum is a maximum or minimum value of a function—the highest peak or lowest valley on a curve.
The plural is extrema.
In calculus, finding extrema involves locating where the derivative equals zero: The function has a local extremum at x = 3.
Global extrema are the absolute highest or lowest values across an entire domain; local extrema are peaks or valleys within a neighborhood.
Uppermost point or culmination
- zenithPoint straight overhead
- pinnacleUtmost summit or spire
- summitPeak or diplomatic gathering
- peakUtmost height attained
climax · acme · crest · upper bound · global maximum · local maximum · optimum · ceiling
Function's rate of change
- critical pointDecisive juncture in events
- turning pointDecisive moment of change
- inflection pointWhere curvature changes sign
- second derivativeChange in rate of change
optimization · gradient · slope · tangent · differentiation · constraint · Hessian · saddle point
Lowest possible point
- troughOpen container for animal feed
- floorIndoor walking surface
- lower boundMinimum possible value
- local minimumLowest nearby, not overall
bottom · valley · depression · low point · absolute minimum · optimization · minimization · descent
Final point reached
- limitMaximum allowed extent
- constraintLimiting condition or rule
- borderOuter edge or limit
- terminusFinal destination point
apex
Uppermost point or culmination
peak · climax · acme · crest · upper bound · global maximum · local maximum · optimum · ceiling · vertex
derivative
Function's rate of change
- critical pointDecisive juncture in events
- turning pointDecisive moment of change
- inflection pointWhere curvature changes sign
second derivative · optimization · gradient · slope · tangent · differentiation · constraint · Hessian · saddle point · local
nadir
Lowest possible point
- troughOpen container for animal feed
- floorIndoor walking surface
- lower boundMinimum possible value
local minimum · bottom · valley · depression · low point · absolute minimum · optimization · minimization · descent
endpoint
Final point reached
- limitMaximum allowed extent
- constraintLimiting condition or rule
- borderOuter edge or limit
terminus · threshold · cutoff · demarcation
- extreme heatSevere high temperature
- extreme sportsHigh-risk recreational activities
- political extremismIdeology at outer fringes
- extreme weatherUnusual, dangerous atmospheric events
- extreme conditionsSeverely challenging environmental situations
- extreme coldSevere low temperature
extreme, extremely, extremist, extremity, extremism, extremer, extremeness, extrema, extremophiles