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 x = x 4 - 8 x 2
First Derivative Test and Local Extrema
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