Question

What is the average rate of change of the function f(x) = 4x – 2 over the interval x = –1 and x = 2?

Answer 1

`4`

Explanation:

Given:
`f(x)=4x-2`

To find: average rate of change of the function
`f(x)=4x-2` over the interval
`x=-1` and
`x=2`

Solution:

Take
`a=-1,\,b=2`

Find
`f(a),\,f(b)`

`f(a)=f(-1)\\=4(-1)-2\\=-4-2\\=-6\\\\f(b)=f(2)\\=4(2)-2\\=8-2\\=6`

Average rate of change of the function
`=(f(b)-f(a))/(b-a)`

`=(f(2)-f(-1))/(2-(-1))\\\\=(6-(-6))/(3) \\\\=(12)/(3)\\\\=4`