### Home > CALC3RD > Chapter Ch5 > Lesson 5.1.3 > Problem 5-30

5-30.

Mr. Lyon is trying to locate the points of inflection for . Since no value of

*exists such that*

*, he assumes there is no change in concavity. Andrew says 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.