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The graph of is shown at right. Determine the intervals where is increasing, decreasing, concave up, and concave down.

We are looking at a graph of , but being asked about the graph of .
So think about what tells us about 

If is positive, then is increasing (and vice versa).
If is increasing, then is concave up (and vise versa).

Continuous curve labeled, f prime of x, coming from lower left, turning at the approximate points (negative 1, comma 3), & (3, comma negative 0.5), passing through the x axis at negative 3, 2, & 4, changing from concave down to concave up at about (1, comma 1).