Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 108x + 6, [−3, 4]

It is convenient to use a graphing calculator for this. The graph shows the maximum and minimum are not at the ends of the interval, so could be found by differentiating the function and setting that derivative to zero. The function would then need to be evaluated for those solutions {-2, 3}.

The absolute minimum on the interval is -237 at x=3.
The absolute maximum on the interval is 138 at x=-2.