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Today's mystery function has these properties: . What do you know about the graph? What don't you know?

When a 1st-derivative is equal to zero at , then is a CANDIDATE for a local max or a local min. When a nd-derivative is equal to zero at , then is also a CANDIDATE for a point of inflection. Obviously, the candidate cannot hold all three positions... so, how do we determine if is a local max, a local min or a POI?