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5-144.

Determine the coordinates of all of the relative extrema and points of inflection for the function .     Homework Help ✎

Max, min, and points of inflection on f(x) will occur where f '(x) = 0 or DNE or f ''(x) = 0 or DNE. But that alone is not enough to determine which is which.

Minima on f(x) happen where f '(x) changes from negative to positive.
Maxima on f(x) happen where f '(x) changes from positive to negative.
Inflection points on f(x) happen where f ''(x) changes sign.

Another way to distinguish between maxima and minima is to use the 2nd Derivative Test.