### Home > APCALC > Chapter 5 > Lesson 5.4.1 > Problem5-141

5-141.

The graph below of $y = f ^\prime(x)$, the derivative of some function $f$, is composed of straight lines and a semicircle. Determine the values of $x$ for which $f$ has local minima, maxima, and points of inflection over the interval $[–3, 3]$.      Homework Help ✎

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.