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local extremum
[local extremum|local extremum] is a point where a function changes direction, indicating a local maximum or minimum.
Definition
local extremum is a point where a function changes direction, indicating a local maximum or minimum. This occurs at critical points where the derivative is zero or undefined, though a critical point alone does not guarantee a local extremum.
Causes
local extremum By Fermat's Theorem, a local extremum occurs at a critical point where either f'(c)=0 or f'(c) is undefined.
Effects
local extremum occurs at a critical point, as Fermat's theorem states that if a local extremum exists at c, then either f'(c)=0 or f'(c) is undefined.