Thread: rate of change problem

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 .
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?

a) The average rate of change is given by:



b) Look for the maximum point of the parabola. This occurs at x = -b/(2a) is the parabola is f(x) =ax^2 +bx + c

Algebraically, differentiate and set the derivative equal to zero, so that the tangent line to the parabola is horizontal. This occurs only at the vertex.

c) Compute h'(x). For increasing intervals, solve h'(x) > 0. For decreasing intervals, solve h'(x) < 0.

Good luck!!