Using Calculus, It Can Be Shown That If a Ball $h = 256 + 16 t - 16 t ^ { 2 }$

Multiple Choice

Using calculus, it can be shown that if a ball is thrown upward with an initial velocity of 16 ft/s from the top of a building 256 ft high, then its height h above the ground t seconds later will be $h = 256 + 16 t - 16 t ^ { 2 }$ During what time interval will the ball be at least 64 ft above the ground?

A) $2 \leq t \leq 5 \mathrm { sec }$
B) $3 \leq t \leq 4 \mathrm { sec }$
C) $0 \leq t \leq 4 \mathrm { sec }$
D) $t \geq 4 \mathrm { sec }$
E) $t \geq 5 \mathrm { sec }$