### Home > CALC > Chapter 6 > Lesson 6.1.1 > Problem6-16

6-16.

Find the point of inflection of $f(x) = x^{1/3}$

$f''(x) = 0$ 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