Category:Definitions/Local Minima

This category contains definitions related to Local Minima.
Related results can be found in Category:Local Minima.

Let $f$ be a real function defined on an open interval $\openint a b$.

Let $\xi \in \openint a b$.

Then $f$ has a local minimum at $\xi$ if and only if:

$\exists \openint c d \subseteq \openint a b: \forall x \in \openint c d: \map f x \ge \map f \xi$

That is, if and only if there is some subinterval on which $f$ attains a minimum within that interval.