A rocket is fired into the air with an initial velocity of 98 m/s. The height ( h ) of the rocket after t seconds is given by the expression $\displaystyle h = 98t - 4.9t2$.

a. What the average rate of change for the first 2 seconds.

b. At what point does the rocket reach its maximum height? Show a graphical and algebraic solution.

c. Over what intervals is the rocket’s height increasing and decreasing?