extrema
Highs and lows
Extrema is the plural of extremum, a mathematical term for the maximum or minimum values of a function.
A local extremum is the highest or lowest point in a neighborhood; a global extremum is the highest or lowest overall.
The function has extrema at x = 0 and x = 4.
Finding extrema is fundamental to calculus and optimization problems.
Function's rate of change
- maximumGreatest permitted quantity
- minimumSmallest possible quantity
- inflectionWord form alteration
- concavityInward-curving surface quality
function · curve · local · global · endpoint · continuity · differentiable · limit
Smallest possible quantity
- valleyLow ground between heights
- nadirLowest possible point
- floorIndoor walking surface
- dipBrief immersion or condiment
bottom · trough · depression · baseline · undershoot
Greatest permitted quantity
- summitPeak or diplomatic gathering
- apexUppermost point or culmination
- zenithPoint straight overhead
- crestHighest point or tuft
vertex · climax · peak · highpoint · ceiling · cap · spike · overshoot
Rate of change across space
- convergenceProcess of approaching sameness
- constraintLimiting condition or rule
- feasibleCapable of being done
- algorithmFinite problem-solving procedure
solver · iteration · heuristic · search · multimodal · nonlinear · stochastic · optimality
Division into two branches
- stabilityResistance to displacement
- cuspPoint of transition
- foldBend onto itself
- singularityPoint where values explode
discontinuity · threshold · nonlinearity · topology · morphogenesis · hysteresis
Able to operate correctly
- geodesicShortest curved-surface path
- stationaryNot in motion
- actionProcess of doing
- integralAntiderivative or crucial component
minimizer · maximizer · admissible · path
derivative
Function's rate of change
- maximumGreatest permitted quantity
- minimumSmallest possible quantity
- inflectionWord form alteration
concavity · function · curve · local · global · endpoint · continuity · differentiable · limit · slope
minimum
Smallest possible quantity
dip · bottom · trough · depression · baseline · undershoot
maximum
Greatest permitted quantity
crest · vertex · climax · peak · highpoint · ceiling · cap · spike · overshoot
gradient
Rate of change across space
- convergenceProcess of approaching sameness
- constraintLimiting condition or rule
- feasibleCapable of being done
algorithm · solver · iteration · heuristic · search · multimodal · nonlinear · stochastic · optimality · fitness
bifurcation
Division into two branches
singularity · discontinuity · threshold · nonlinearity · topology · morphogenesis · hysteresis
functional
Able to operate correctly
- geodesicShortest curved-surface path
- stationaryNot in motion
- actionProcess of doing
integral · minimizer · maximizer · admissible · path
- extremesbest, worst, biggest, smallest, highest
- calculusderivatives, integral, integrals, limits, differential calculus
- Chebyshev polynomialsrecurrence relation, orthogonality, zeros, coefficients
- function propertiesdomain, range, continuity, derivative, limit
- temperaturacaliente, tibia, maxima, minima, corporal
- extreme heatSevere high temperature
- extreme sportsHigh-risk recreational activities
- extreme weatherUnusual, dangerous atmospheric events
- extreme conditionsSeverely challenging environmental situations
- extreme coldSevere low temperature
- extreme povertyIncome below survival threshold