### Home > CALC > Chapter 6 > Lesson 6.1.1 > Problem 6-16

6-16.

Find the point of inflection of *f*(*x*) = *x*^{1/3}. Homework Help ✎

*f* ''(*x*) = 0 and *f* ''(*x*) = DNE will identify CANDIDATES for points of inflection.

To determine if a candidate is the location of the POI, you could either:

1. Evaluate *f* ''(*x*) before and after *x* = candidate. If there is a sign change, then the candidate is the *x*-value of a POI.

2. Evaluate *f* '''(candidate). If the 3rd-derivative does not equal zero, then the candidate is the *x*-value of a POI.

POI at (0,0).

Be sure to show all steps and justification/tests.

Use the eTool below to visualize the problem.

Click the link at right for the full version of the eTool: Calc 6-16 HW eTool