See attached file for full problem description.
Find the interval on which the function 2 2 ( ) ( 2) ( 3) f x x x = − + is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima. Any global extrema should also be identified.
Please see attached files.
The critical points are where the slope to the function is zero. Here you can plot the graph as I did in the excel file. From the graph we can see:
Local minima: (-3,0) and (2,0)
Local maximum: (-0.5,39)
The intervals include:
x ≤ -3: f(x) decreasing
-3 ≤ x ≤ ...
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