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Find the interval on which the function

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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.

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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 ≤ ...

Solution Summary

The solution provides detailed explanations and instructions, including plots in Excel, for this problem.