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Mr. Lyon is trying to locate the points of inflection for f(x) = 3x2/3. Since no value of x exists such that f ″(x) = 0, 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 y = f(x) to verify your answer. Homework Help ✎

CANDIDATES for points of inflection can be found where f ''(x) = 0 and where f ''(x) = DNE. You must check both.

Answer Graph

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