Question

Find the average rate of change of f(x)=2x-1 from x=-1 to x=2

Answer 1

The average rate of change from x = -1 to x = 2 is 2

Solution:

Given function is:

f(x) = 2x - 1

We have to find the average rate of change from x = -1 to x = 2

The average rate of change is given as:

`\text {Average rate of change}=(f(b)-f(a))/(b-a)`

The average rate of change from x = -1 to x = 2 is given by formula:

`\text {Average rate of change}=(f(2)-f(-1))/(2-(-1))\\\\\text {Average rate of change}=(f(2)-f(-1))/(3)`

Find f(2) and f( - 1)

Substitute x = 2 in given function

f(2) = 2(2) - 1 = 4 - 1 = 3

Substitute x = -1 in given function

f( - 1) = 2(-1) - 1 = -2 - 1 = -3

Substitute the values in above formula,

`\text {Average rate of change}=(3-(-3))/(3)=(6)/(3)=2`

Thus average rate of change from x = -1 to x = 2 is 2