A stone is projected vertically upward from ground level. Its height (in metres) above the ground after t seconds is modeled by
s(t)=−t3+6t2+15t+2,0≤t≤6.
(i) Identify all critical points of s(t) in the interval [0,6].
(ii) Classify each critical point as a point of local maximum or local minimum with suitable justification.
(iii) Determine the greatest height attained by the stone and the time at which it occurs.
(iv) Find the least height (relative extremum) reached within the interval [0,6], if any, and specify the corresponding time.