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

Max, min, and points of inflection on will occur where or DNE or or DNE. But that alone is not enough to determine which is which.

Minima on happen where changes from negative to positive.
Maxima on happen where  changes from positive to negative.
Inflection points on happen where  changes sign.

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