### Home > CALC > Chapter 6 > Lesson 6.1.1 > Problem 6-15

6-15.

Sketch a continuous function with the following properties: ,

*does not exist,*

*for*

*and*

*for*

*.*

Translation: the slope of is zero at

*. Note:*

*is a CANDIDATE for local max or min. (It might also be a point of inflection.)*

Reasons why a derivative might not exist at a point:

cusp

endpoint

jump

hole

vertical tangent

for

*and*

*for*

Translation: There is a change in concavity at .