Definition:Stationary Point
Definition
Let $f$ be a real function which is differentiable on the open interval $\left({a \,.\,.\, b}\right)$.
Let $\exists \xi \in \left({a \,.\,.\, b}\right): f^{\prime} \left({\xi}\right) = 0$, where $f^{\prime} \left({\xi}\right)$ is the derivative of $f$ at $\xi$.
Then $\xi$ is known as a stationary point of $f$.
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): $\S 11.3$
