3.4E: Rates of Change and Behavior of Graphs (Exercises)
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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.
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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 \(\PageIndex{3}\).