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

5-141.

The graph below of , the derivative of some function

*, is composed of straight lines and a semicircle. Determine the values of*

*for which*

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

You are looking at the graph of .

A minimum value on is where the

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