### Home > CALC > Chapter 5 > Lesson 5.1.3 > Problem 5-30

5-30.

Mr. Lyon was trying to find the points of inflection for *f*(*x*) = 3*x*^{2/3}. Since no value of *x* existed such that *f* ′′(*x*) = 0, he assumed there was no change in concavity. Andrew said 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 *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.

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