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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 .      

You are looking at the graph of , but you are being asked to describe 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  occur where changes the sign of its slope. This happens twice.