Find the possibility graph of its derivative f'.
The possibility graph of its derivative f' is
The given information is
From the above graph, f'>0 at (- ∞, - 1) and (2, ∞) ; the function is increasing from (- ∞, - 1) and (2, ∞) ; the graph f' <0 at (-1,2) where the function is decreasing.
Sketch careful, labeled graphs of each function f in Exercises 63–82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of and examine any relevant limits so that you can describe all key points and behaviors of f.
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