Question

Find the average rate of change
f(x)=x^2−6x+8 when x2=1 and x1=3

Answer 1

Average rate of change for given function is: -2

Explanation:

Given function is:

`f(x)=x^2-6x+8\\x_12= 1\\x_1 = 3`

In order to find the rate of change, we have to find the value of function on x1 and x2

So,

`f(x_1) = (3)^2-6(3)+8 = 9-18+8 = -1\\f(x_2) = (1)^2-6(1)+8 = 1-6+8 = 3`

The formula for finding the rate of change is:

`Rate\ of\ change = (f(x_2)-f(x_1))/(x_2-x_1)`

Putting the values, we get

`=(3-(-1))/(1-3)\\=(3+1)/(-2)\\=(4)/(-2)\\= -2`

Hence,

Average rate of change for given function is: -2