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?