stationary point: meaning, definition, pronunciation and examples
C1technical (mathematics, physics, engineering), formal academic
Quick answer
What does “stationary point” mean?
A point on a curve where the derivative is zero.
Audio
Pronunciation
Definition
Meaning and Definition
A point on a curve where the derivative is zero; the function's rate of change is momentarily zero.
In mathematics (especially calculus and optimization), a point where the tangent to the curve is horizontal. It can be a local maximum, local minimum, or a point of inflection. In physics and engineering, it can refer to a point of equilibrium where a system is not changing.
Dialectal Variation
British vs American Usage
Differences
No significant difference in technical meaning or usage. British English may be more likely to use the synonym 'turning point' in certain A-level/GCSE educational contexts for local maxima/minima.
Connotations
Neutral technical term in both varieties.
Frequency
Equally common in academic and technical texts in both regions.
Grammar
How to Use “stationary point” in a Sentence
The function HAS a stationary point AT x=2.We FIND the stationary points BY differentiating.The stationary point IS CLASSIFIED AS a maximum.Vocabulary
Collocations
Examples
Examples of “stationary point” in a Sentence
verb
British English
- The curve stations briefly at the point x=5 before descending again. (Rare, metaphorical)
American English
- The function's value stations at a local maximum. (Rare, metaphorical)
adverb
British English
- The graph behaved stationarily near x=0. (Highly technical/rare)
American English
- The derivative vanished stationarily. (Highly technical/rare)
adjective
British English
- The stationary-point analysis revealed two potential optima.
American English
- We need to consider the stationary-point behaviour of the system.
Usage
Meaning in Context
Business
Rare. Potentially in analytical contexts: 'We've reached a stationary point in our growth curve.'
Academic
Common in mathematics, physics, and engineering lectures, textbooks, and problem sets.
Everyday
Virtually never used.
Technical
Core term in calculus, optimization, dynamical systems, and thermodynamic analysis.
Vocabulary
Synonyms of “stationary point”
Strong
Neutral
Weak
Vocabulary
Antonyms of “stationary point”
Watch out
Common Mistakes When Using “stationary point”
- Confusing 'stationary' (not moving) with 'stationery' (writing materials). Misspelling as 'stationery point'. Using it to mean 'a fixed location' in non-mathematical contexts.
FAQ
Frequently Asked Questions
No. A stationary point can be a local maximum, a local minimum, or a point of inflection (like on the curve y=x^3 at x=0).
In many contexts, they are used interchangeably. However, some definitions reserve 'critical point' for where the derivative is zero OR undefined, while 'stationary point' specifically requires the derivative to be zero.
Take the first derivative of the function, set it equal to zero, and solve the resulting equation for the variable(s).
Yes, a function can have multiple stationary points (e.g., a polynomial of degree n can have up to n-1 stationary points).
A point on a curve where the derivative is zero.
Stationary point is usually technical (mathematics, physics, engineering), formal academic in register.
Stationary point: in British English it is pronounced /ˈsteɪʃ(ə)n(ə)ri pɔɪnt/, and in American English it is pronounced /ˈsteɪʃəˌnɛri pɔɪnt/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “The function levels off at a stationary point.”
- “The graph flattens out at the stationary point.”
Learning
Memory Aids
Mnemonic
Think of a car (the function) coming to a temporary, complete stop (stationary) on a hill (the curve). That stop is the stationary point.
Conceptual Metaphor
A FUNCTION IS A JOURNEY; A STATIONARY POINT IS A PAUSE OR A REST STOP ON THAT JOURNEY.
Practice
Quiz
What is a stationary point?