The position of a model rocket moving vertically is s(t)=10t−t2 meters for 0≤t≤10, where t is measured in seconds.
(a) Determine all times t in [0,10] at which the rocket is momentarily at rest.
(b) Find the time at which the rocket is highest above the ground on the interval [0,10], and calculate that maximum height.
(c) Verify that the value found in part (b) is indeed the absolute maximum on the given interval by comparing it with the rocket’s height at any other relevant times.