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Refer to the graph at right of , the derivative of some function .

  1. Where is increasing? How can you tell?

    Notice that this is the graph of , the slopes of , and will increase where its slopes are positive.

  2. Approximate the interval over which is concave up. Justify your conclusion with the graph.

    Eyeball to see where you believe the point of inflections are in order to approximate the intervals.  Note: Concave up is a U shape.

  3. Is positive or negative? Explain how you know.

    represents the slopes of the given graph, . So look at the graph. Does it have a positive or a negative slope at ?

Continuous curve, starting in upper left, concave up, turning at the approximate points, (negative 2.5, comma negative 7), & (4, comma 5.5), passing through the x axis at negative 5, 1, & negative 6, changing concavity at (1, comma 0).