William W. answered • 09/13/20
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This is just a matter of graphing the function on your calculator and looking at the graph to answer the questions. If you need help doing that, let me know and I'll be happy to offer a complimentary tutoring session so I can show you how. If you don't have a graphing calculator then you can use desmos online (just google it).
The graph looks like this:
William W.
Although the graph does not show the y values at x = -15 and x = 15, it does show the trend toward negative and positive infinity. Please note that nowhere in the question does it ask about the absolute extrema on the interval, only the local extremes. The graph was tailored so the student could easily see what was being asked in the problem.
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09/13/20
Tom K.
William, you should edit your graph, as it does not show x ranging from -15 to 15. As f(-15) = 5376.53 is the maximum and f(15) = -3601.15, I would use -6000 to 6000 (unless your graph is all positives or all negatives, I would normally make the range symmetric in order to prevent misinterpretations). Note how having a relatively large linear coefficient plus it having a sign opposite that of the cubic term drives us toward the shape of this graph. I would hope that a graphing calculator would have a default for the y range once you specify the x range, but if it does not, you could always plot first in Excel or desmos, as William recommends.09/13/20