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3.3E: Rates of Change and Behavior of Graphs (Exercises)

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    56071
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    For the following exercises, find the average rate of change of the functions from \(x=1\) to \(x=2\).

    24. \(f(x)=4 x-3\)
    25. \(f(x)=10 x^{2}+x\)
    26. \(f(x)=-\frac{2}{x^{2}}\)

    For the following exercises, use the graphs to determine the intervals on which the functions are increasing, decreasing, or constant.

    27

    Graph of a parabola.

    28.

    Graph of a cubic function.

    29.

    Graph of a function.

    30. Find the local minimum of the function graphed in Exercise 3.27 .
    31. Find the local extrema for the function graphed in Exercise 3.28 .
    32. For the graph in Figure \(\PageIndex{3}\), the domain of the function is [-3,3] . The range is [-10,10] . Find the absolute minimum of the function on this interval.
    33. Find the absolute maximum of the function graphed in Figure \(\PageIndex{3}\).

    Graph of a cubic function.
    Figure \(\PageIndex{3}\)

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