Question

The height of a rocket t seconds after launch is modeled by the function: f(t)=-16t^2+72t.

What is the maximum height of the rocket in feet?

Answer 1

Explanation:

the extreme values of a function happen at the zeros of the first derivation of that function.

f(t) = -16t² + 72t

f'(t) = -2×16t + 72 = -32t + 72

0 = -32t + 72

32t = 72

t = 72/32 = 2.25 seconds

f(2.25) = -16(2.25)² + 72×2.25 = -16×5.0625 + 72×2.25 =

= -81 + 162 = 81 ft

so, the rocket reaches its maximum height of 81 ft after 2.25 seconds of flight.