Question

An object is launched upward at 64 ft/sec from a platform that is 80 feet high. What is the objects maximum height if the equation of height (h) in terms of time (t) of the object is given by h(t) = -16t2 + 64t + 80?

Answer 1

7?

Answer 2

When does the height stop changing?

This is the same thing as asking, when does h stop increasing and starts decreasing.

Or in other words, when is
$$
{dh(t)\over dt}=0
$$
Hence, the change in height becomes zero when its derivative is zero.

So find this derivative, set equal to zero and solve for \(t\)

Answer 3

Does this make sense?