The altitude (in feet) of a model rocket tt sec into a trial flight is given by the following equation.

 s = f(t) = −4t ³ + 24t ² + 4 (t ≥ 0)

a. Find an expression for the rocket's velocity vv at any time tt .

b. Compute the rocket's velocity when t = 0, 2, 4, and 6. Interpret your results.

c. Using the results from the solution to part (b), find the maximum altitude attained by the rocket. Hint: At its highest point, the velocity of the rocket is zero.