Let f(x)=x3−6x2+9x+2 for 0≤x≤4.
(a) Determine all critical numbers of f that lie in the open interval (0,4).
(b) Evaluate f at every critical number found in part (a) and at the endpoints of the interval. Show all work.
(c) Identify the absolute maximum value and the absolute minimum value of f on [0,4], and state the x–coordinates where they occur.