Local extrema exists at a point where the derivative
of a function changes sign. The function has a local MAXIMUM at a
critical point of the derivative changes from positive to
negative. The function has a local MINIMUM if the derivative
changes from negative to positive. The First Derivative Test for
local extrema is used to determine if the function has a local
maximum or minumum value at that crtitical point.

Here we use that test to find the local extrema for the function: $f\left(x\right)={x}^{4}-8{x}^{2}$

Here we use that test to find the local extrema for the function: $f\left(x\right)={x}^{4}-8{x}^{2}$

First Derivative Test and Local Extrema

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