# 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

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.