Use the maximum/minimum finder on a graphing calculator to determine the approximate location of all local extrema of the function. \( f(x)=0.02 x^{5}+0.2 x^{4}-x^{3}-5 x^{2}+5 x+40 \)

To find the local extrema of the function \( f(x) = 0.02 x^{5} + 0.2 x^{4} - x^{3} - 5 x^{2} + 5 x + 40 \), first, input the function into the graphing calculator. Next, use the "Graph" feature to visualize the function, then access the "Calculate" option. Select "Maximum" or "Minimum" as needed, and move the cursor to the approximate location of the extrema, defining a left and right bound before letting the calculator find the exact location for you. Make sure you check both the "Maximum" and "Minimum" calculators, as local maxima and minima can appear near each other on the graph. Observing the changes in the graph helps you identify whether you need to adjust your bounds for accurate calculations. The more you explore graphically, the better you'll get at recognizing patterns and shapes of local extrema for various functions!