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Mr. Lyon is trying to locate the points of inflection for . Since no value of exists such that , he assumes there is no change in concavity. Andrew says that a point of inflection exists where the second derivative changes sign. Who is correct and why? Use the second derivative and the graph of to verify your answer.

CANDIDATES for points of inflection can be found where  and where DNE. You must check both.

Continuous piecewise labeled, f of x, coming from upper left, concave down, turning at the origin, continuing concave down, up & right.

Notice that there is not a concavity change at the cusp.