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
 
 The maximum height is:
 h (4) = 256 feet