h(t)=-16t^2+96t+112
The arrow reaches maximum height when the slope of the curve equals zero.
The slope can be found by taking the first derivative:
h’(t)=-32t+96
h’(t)=
0 when t = 3
h(3)=-16(3^2)+96(3)+112 = -144 + 288 + 112 = 256
So 256 feet is the maximum height.