Local Minimum: Meaning, Notation, and Example
A function value at most as large as nearby values.
Definition and meaning
A local minimum is defined relative to a neighborhood and need not be the smallest value on the whole domain.
The term local minimum names a precise mathematical idea, not merely a visual pattern. Read its notation as a statement with hypotheses, quantities, and a conclusion.
Notation
Read every symbol with its domain and hypotheses; notation compresses an argument but does not remove its conditions.
Worked example
Identify the quantities in the notation, state the relevant hypothesis, and explain what conclusion the local minimum statement permits.
Common confusion
Do not treat local minimum as a keyword that automatically selects a formula; its hypotheses and domain still control the conclusion.