It’s a toy rocket launch vertically upward from ground level with an initial velocity of 128 ft per second then it’s height h after t seconds is given by the equation h(t)=-16t^2+128t

Answer 1

maximum height is reached when h'(t) = 0

-32t +128 = 0

32t=128

t=128/32 = 64/16 = 4 seconds

the derivative is the velocity which = 0 when it's at a maximum height

In 4 seconds the rocket reaches a height of

h=--16(4)^2 +128(4) =4(-64+128) = 4(64) = 256 feet

It comes back to ground level in another 4 seconds