Let f(x)=x3−6x2+9x+5 be defined on the closed interval [0,4].
a. (i) Find f′(x) and hence obtain all critical points that lie inside the interval [0,4].
b. (ii) Classify each critical point obtained in part (i) as a local maximum or a local minimum.
c. (iii) Evaluate f(x) at every critical point and at the endpoints x=0 and x=4. Hence determine the absolute maximum and absolute minimum values of f on the interval [0,4], stating the points at which they occur.