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5-43.

Using the graph of the slope function at right, determine where the following situations occur for : Homework Help ✎

Notice that this is a graph of , but you are being asked about .

  1. Relative minima.

    Relative minima and maxima can exist when .
    This occurs when , and . But which points indicate a maximum and which indicate a minimum?

    A minimum occurs when the slope changes from negative to positive.

  1. Relative maxima.

    See the hint in part (a). A maximum occurs when the slope changes from positive to negative.

  1. Interval(s) over which is increasing.

    is increasing when .

  1. Inflection points.

    Inflection points can happen where . Remember, we are looking at the graph of .

  1. Interval(s) over which is concave up.

    is concave up when .

  1. Interval(s) over which is concave down.

    is concave down when is decreasing.