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local extrema
[local extrema|local extrema] are points where a function attains a maximum or minimum value relative to its neighboring points.
Definition
local extrema are points where a function attains a maximum or minimum value relative to its neighboring points. These points are referred to as local extrema, which includes two minima and one maximum in the given example.
Mechanism
local extrema are points on a function's graph where the function changes from increasing to decreasing or vice versa. To identify them, analyze the graph's slope changes using a graphing utility.
Effects
Observations lead to a formal definition of local extrema. The graph can be used to estimate these extrema and identify intervals where the function is increasing.