Category:Definitions/Turning Points
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This category contains definitions related to Turning Points.
Related results can be found in Category:Turning Points.
Local Maximum
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 maximum at $\xi$ if and only if:
- $\exists \openint c d \subseteq \openint a b: \forall x \in \openint c d: \map f x \le \map f \xi$
That is, if and only if there is some subinterval on which $f$ attains a maximum within that interval.
Local Minimum
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.
Pages in category "Definitions/Turning Points"
The following 5 pages are in this category, out of 5 total.