(a) Average rate of change for , and .

Average rate of change of  on the interval .

Average rate of change of  on the interval .

Observe the graph:

The values of

Average rate of change on the time interval is .

Average rate of change of  on the interval .

Observe the graph:

The values of

Average rate of change on the time interval is . 

Average rate of change of  on the interval .

Observe the graph:

The values of

Average rate of change on the time interval is .

(b) The object is increasing in speed, or accelerating, along all three intervals. It is accelerating at the faster rate for . While it is very slowly accelerating for the interval , it is still increasing its speed.

(c) Steep graph = high magnitude rate of change = rapidly increasing or decreasing; flat graph = low magnitude rate of change = minimal increasing or decreasing.

(a) Average rate of change on the time interval is .

Average rate of change on the time interval is .

Average rate of change on the time interval is .

(b) The object is increasing in speed, or accelerating, along all three intervals. It is accelerating at the faster rate for . While it is very slowly accelerating for the interval , it is still increasing its speed.

(c) Steep graph = high magnitude rate of change = rapidly increasing or decreasing; flat graph = low magnitude rate of change = minimal increasing or decreasing.