Consider the polynomial function f(x)=x3−6x2+9x+4 defined on the closed interval [0,5]. For your calculations you may use the derivative f′(x)=3x2−12x+9.
(i) Find all values of x in (0,5) that satisfy f′(x)=0.
(ii) Evaluate f(x) at each point obtained in part (i) as well as at the endpoints x=0 and x=5.
(iii) Determine the absolute maximum value and the absolute minimum value of f on [0,5], stating the points at which these values occur.