local minimum
[local minimum|local minimum] [local minimum] is a point where the function attains its lowest value within a specific interval, as indicated by the presence of a local minimum at 3.
Definition
local minimum [local minimum] is a point where the function attains its lowest value within a specific interval, as indicated by the presence of a local minimum at 3.
Mechanism
local minimum The local minimum occurs at x = 1 and x = 3. Critical points are identified by where f' switches sign from negative to positive, indicating a local minimum. The function's behavior is analyzed through these critical points and absolute extrema.
Effects
local minimum The local minimum at x = 3 occurs because f' switches sign from negative to positive as x increases. This confirms the results found in step 6 regarding concavity, combining information about f' (x) = 0 at local extrema.