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

6-16.

Locate the point of inflection on the graph of $f(x) = x^{1/3}$. 6-16 HW eTool (Desmos). Homework Help ✎

$f^{\prime\prime}(x) = 0$ and $f^{\prime\prime}(x) = \text{DNE}$ will identify CANDIDATES for points of inflection.
To determine if a candidate is the location of the Point of Inflection, you could either:
1. Evaluate $f^{\prime\prime}(x)$ before and after $x =$ candidate. If there is a sign change, then the candidate is the x-value of a POI.
2. Evaluate $f^{\prime\prime\prime}$(candidate). If the 3rd-derivative does not equal zero, then the candidate is the x-value of a POI.

Point of Inflection 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