A toy rocket is shot vertically into the air from a launching pad 6 feel above the ground with an initial velocity of 64 feet per second. The height h, in feet, of the rocket above the ground as t seconds after launch is given by the function h(t)=-16t^2+64t+6. How long will it take the rocket to reach its maximum height? What is the maximum height?

How long will it take the rocket to reach its maximum height?

What is the maximum height?

Step-by-step explanation:

h(t) = -16t² + 64t + 6

in order to determine the maximum height we must find the derivative:

h'(t) = 2 · -16t + 64 = -32t + 64

0 =  -32t + 64

32t = 64

t = 64/32 = 2 seconds

just replace t by 2 in order to determine the maximum height:

maximum height = -16·2² + 64·2 + 6 = -64 + 128 + 6 = 70 feet