To determine the maximum height, h, from the given above. Differentiate the function and equate to zero. Then, determine the value of t. The value, when substituted to the original function, will give the maximum height. For this given,
dh(t)/dt = -32t + 128 = 0, t = 4
Substituting t = 4 to the original function gives 320. Thus, the maximum height is 320 units.