Answer:
The absolute maximum value of f on [-2, 4] occurs at x = 4.
Explanation:
We know that the absolute maximum value of f(x) on this interval will occur at either a critical point or an endpoint. The critical points are any point where f'(x) is either equal to zero or not defined. Since f is a polynomial, f'(x) = 3x^2 - 6x is always defined, but is equal to zero at x = 0 and x = 2. We can check the value of f(x) at each critical point and endpoint:
f(-2) = -8
f(0) = 12
f(2) = 8
f(4) = 28
Therefore, f has an absolute maximum value of 28 on the closed interval [-2, 4], which occurs when x = 4.