### 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 *f* '(*x*), but you are being asked to describe the graph of *f*(*x*).

A minimum value on *f*(*x*) is where the *y*-values change from decreasing to increasing. How does that show up on the *f* '(*x*) graph?

Local minima on *f*(*x*) are located anywhere that the graph of *f* '(*x*) changes from negative to positive. Local maxima are the reverse.

Points of inflection on *f*(*x*) occur where *f* '(*x*) changes the sign of its slope. This happens twice.