2. Method 2: Suppose we now choose to approximate the rate of change of the height of the ball during its flight by imagining the constant rates associated with a sliding interval of width h = 0.3 seconds, that always begins at the current value of x and extends 0.3 seconds ahead. That is, for every value of x, we find an approximate rate of change by using the average rate of change for the interval

.

a. What is the constant rate of change that would be used at each of the following moments

(estimate numerically by drawing the appropriate segments onto the graph above)

i. At the moment x = 0.1 sec, the approximate CROC of the height is _____________

ii. At the moment x = 0.25 sec, the approximate CROC of the height is ____________

iii. At the moment x = 0.45 sec the approximate CROC of the height is ____________

iv. At the moment x = 0.8 sec, the approximate CROC of the height is ____________

v. Why can we not use this method to approximate the CROC of the height at the

moment x = 1.1 sec in this example ?

A ball is thrown upward, and its height is monitored as time goes by. Below at right is the graph of the ball's height in meters as a function of time since being thrown, in seconds. Our aim (2 methods) is to approximate the rate of change of the height of the ball during its flight. feet/sec feet 2 0.2 0.4 0.6 0.8 1.2 -24 012 0.4 0.5