Definition:Stationary Point

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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


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