Critical Number: Meaning, Notation, and Example
A domain input where the derivative is zero or does not exist.
Definition and meaning
Critical numbers are candidates for extrema, not automatic maxima or minima.
The term critical number 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 critical number statement permits.
Common confusion
Do not treat critical number as a keyword that automatically selects a formula; its hypotheses and domain still control the conclusion.