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

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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.

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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.