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Question

If a stone is dropped from a height of 576 ​ft, then its height​ (in feet) above the ground is given by the function

​h(t)= -16t^2 + 576 where t is time​ (in seconds). To get an idea of how fast the stone is traveling when it hits the​ ground, find the average rate of change of the height on each of the time intervals

​[0,6​] ​[1,6​] ​[5.9​,6​] [5.99​,6​], and [5.999,6​].

Answer 1

The average rate of change is just the slope of the line connecting the endpoints of the interval. For example, h(0) = 576 and h(1) = 560, so the average rate of change on [0,1] is (560 - 576) / (1 - 0) = -16.