### Home > CALC > Chapter 5 > Lesson 5.4.1 > Problem 5-141

5-141.

Given the graph of below, determine the values of

*for which*

*has local minima, maxima, and points of inflection on the interval*

You are looking at the graph of , but you are being asked to describe the graph of

*.*

A minimum value on is where the

*y*-values change from decreasing to increasing. How does that show up on the

*graph?*

Local minima on are located anywhere that the graph of

*changes from negative to positive. Local maxima are the reverse.*

Points of inflection on occur where

*changes the sign of its slope. This happens twice.*