Determine which function has the greatest rate of change over the interval [0, 2].

Remember that the average rate of change of a function over an interval is the slope of the straight line connecting the end points of the interval. To find those slopes, we are going to use the slope formula: 

Rate of change of :
From the graph we can infer that the end points are (0,1) and (2,4). So lets use our slope formula to find the rate of change of :




The average rate of change of the function  over the interval [0,2] is 1.5

Rate of change of :
Here the end points are (0,0) and (2,2)



The average rate of change of the function  over the interval [0,2] is 1

Rate of change of :
Here the end points are (0,-1) and (2,0)



The average rate of change of the function  over the interval [0,2] is 0.5

Rate of change of :
Here the end points are (0,0.5) and (2,2.5)



The average rate of change of the function  over the interval [0,2] is 1

We can conclude that the function that has the greatest rate of change over the interval [0, 2] is the function a.