A ball is tossed into the air from ground level at 128 feet per second. The function f(t)...

A ball is tossed into the air from ground level at 128 feet per second. The function f(t) = −16t2 + 128t gives the height above ground (in feet) as a function of time (in seconds).

a. Find f(0) and f(3).

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b. How far did the ball travel in the first three seconds of its flight?

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c. Find the average rate of change of the height for the time interval [0, 3].

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d. Find

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e. Find

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f. Find the instantaneous rate of change of the height (or the instantaneous velocity) of the ball at times t = 0, 2, 4, 6, and 8 seconds.

The average rate of change of the function f on the interval [c, x] is