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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 .      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.