Part 5/6:
At ( x = -1 ): ( f' ) changes from negative to positive → Local Minimum.
At ( x = 0 ): ( f' ) changes from positive to negative → Local Maximum.
At ( x = 2 ): ( f' ) remains positive → Neither.
Graphical Representation
To visualize our results, we could graph the function ( f(x) ) and observe the turning points identified through our analysis. The graph would illustrate a local maximum at ( (0, 5) ), a local minimum at ( (-1, 0) ), and confirm that ( (2, -27) ) is neither a maximum nor a minimum.