### Home > CALC > Chapter 5 > Lesson 5.2.4 > Problem 5-98

5-98.

Using the graph of , determine the values of

*where*

*has a local minimum, local maximum or point of inflection. Justify your answer for each point.*

You are looking at a graph of , which shows all the slopes of

*.*

A local minimum on is located where the slopes of

*change from negative to positive.*

A local maximum on is located where the slopes of

*change from positive to negative.*

An inflection point on is where concavity changes, and concavity is a determined by the slope of the the slopes.

: local minimum

*: local maximum*

*: inflection point*