Question

On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine burns out. The rocket's height, h, in feet above the surface of the lake, is given by the equation, h = -16t 2 + 64t + 80, where t is time in seconds. The maximum height of the rocket is how many feet.

Answer 1

h'(x)=-32t+64, the only zero of that is 2, and it goes from positive to negative, so the maximum height will be at time 2. Plug in 2 to the original equation and that gives you 144. The max height is 144 feet.