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

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

• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 11.3$