Definition:Stationary Point
Definition
Let $f$ be a real function which is differentiable on the open interval $\openint a b$.
Let $\exists \xi \in \openint a b: \map {f'} \xi = 0$, where $\map {f'} \xi$ is the derivative of $f$ at $\xi$.
Then $\xi$ is known as a stationary point of $f$.
Also known as
A stationary point is also known (mainly in USA) as a critical point.
Notes
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It follows from Derivative at Maximum or Minimum‎ that any local minimum or local maximum is a stationary point.
However, it is not the case that a stationary point is always either a local minimum or local maximum.
Sources
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 11.3$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: critical point: 1.
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Entry: stationary point: 1a.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Entry: stationary point (critical point): 1.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Entry: stationary point (critical point): 1.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: stationary point (in one variable)