Question

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

Answer 1

what the other guy said

Explanation:

Answer 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:
`m= (y_(2)-y_(1))/(x_2-x_1)`

Rate of change of
`a`:
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
`a`:

`m= (y_(2)-y_(1))/(x_2-x_1)`

`m= (4-1)/(2-0)`

`m= (3)/(2)`

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

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

`m= (2-0)/(2-0)`

`m= (2)/(2)`

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

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

`m= (0-(-1))/(2-0)`

`m= (1)/(2)`

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

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

`m= (2.5-0.5)/(2-0)`

`m= (2)/(2)`

`m=1`
The average rate of change of the function
`d` 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.