Question

In which of the following intervals is the average rate of change greater for f than for g

Answer 1

Answer: Option B

[3, 5]

Explanation:

The function g(x) is a line of slope m = 4. Therefore, its rate of change is constant and equal to 4.

The rate of change of the function f(x) in the interval
`[x_1, x_2]` is calculated with the following formula

`m =(y_2-y_1)/(x_2 - x_1)`

Note that the rate of change of the function increases as x increases.

For example

For [-1, 0]

`m =(4-3.5)/(0 - (-1))`

`m =(1)/(2)`

`(1)/(2)<4`

For [0, 2]

`m =(7-4)/(2 - 0)`

`m =(3)/(2)`

`(3)/(2)<4`

For [1, 3]

`m =(11-5)/(3-1)`

`m =3`

`3<4`

For [3, 5]

`m =(35-11)/(5-3)`

`m =12`

`12>4`