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5-70.

Today's mystery function has these properties: f ″(−3) = f ′(3) = f(−3) = 0. What do you know about the graph? What don't you know? Homework Help ✎

When a 1st-derivative is equal to zero at x = a, then x = a is a CANDIDATE for a local max or a local min. When a 2nd-derivative is equal to zero at x = a, then x = a is also a CANDIDATE for a point of inflection. Obviously, the candidate cannot hold all three positions... so, how do we determine if x = a is a local max, a local min or a POI?