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

5-30.

Mr. Lyon was trying to find the points of inflection for . Since no value of

*existed such that*

*, 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*

*to verify your answer.*

CANDIDATES for points of inflection can be found where and where

*DNE. You must check both.*

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