Flight of a Rocket The altitude in feet attained by a model rocket t seconds into flight is given by the function h(t). Find the maximum altitude (in ft) attained by the rocket. (Round your answer to the nearest foot.) h(t) = − 1 3 t3 + 2t2 + 12t + 21 (t ≥ 0)

Step-by-step explanation:

The maximum altitude of the rocket can be found with the help of First Derivative and Second Derivative Tests:

Critical values are:

,

The second derivative values related to critical values are:

(Maximum)

(Minimum)

Only the first solution offers a physically reasonable solution, as time is a positive variable. Then, maximum height is:

36

step-by-step explanation: