If a projectile is fired straight upward from the ground with an initial speed of 128 feet per second, then its height h in feet after t seconds is given by the function h (t) equalsnegative 16 t squared plus 128 t. find the maximum height of the projectile.

For this case we have the following function:

h (t) = - 16t ^ 2 + 128t

Deriving the function we have:

h ' (t) = - 32t + 128

Equaling zero we have:

-32t + 128 = 0

We clear the time:

t = 128/32

t = 4

Substituting in the height equation:

h (4) = - 16 * (4) ^ 2 + 128 * (4)

h (4) = 256 feet

Answer:

The maximum height is:

h (4) = 256 feet