The height (in meters) of a drone above the ground during a test flight is modeled by
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The height (in meters) of a drone above the ground during a test flight is modeled by h(t)=t3−9t2+24t+5, where t is the time in minutes since takeoff. The flight lasts from t=0 to t=8 minutes.
(a) Determine all critical points of h in the closed interval [0,8].
(b) Evaluate h at each critical point and at the endpoints of the interval. Identify the time at which the drone reaches its maximum altitude and state that altitude.
(c) Provide a justification that the value you found in part (b) is indeed the absolute maximum height on the interval [0,8].