Let f(x)=3x3−2x2+4 defined on the closed interval [−1,4].
(a) Determine all critical points of f in the interval [−1,4] and classify each as a point of local maximum, local minimum, or neither.
(b) Verify whether there is exactly one critical point in (−1,4). State your reasoning clearly.
(c) Using only the information established in parts (a) and (b) together with any relevant properties of continuous functions on a closed interval, determine the absolute maximum and absolute minimum values of f on [−1,4]. Justify your conclusions.