Question

Find the average rate of change of the function f ( x ) = 1 x 2 + 2 x + 2 , on the interval x ∈ [0,2].

Answer 1

The given function is

`f(x) = x^2 +2x+2`

First we have to find f(0) and f(2).

And for that, we put 0 and 2 for x. That is,

`f(0)=0^2+2(0)+2, f(2) =2^2 +2(2) +2  \\ f(0) = 2, f(2) = 10`

Now we use the formula for average rate of change, which is

`\frac{f(2)-f(0)}(2-0} = (10-2)/(2-0) = (8)/(2) = 4`

Answer 2

Given :
`f ( x ) = x^2 + 2 x + 2`

Formula for average rate of change is

`Average =(f(x_2)-f(x_1))/(x_2-x_1)`

x1 and x2 is the given interval.

Given interval is [0,2].

x1 = 0, x2=2

`f ( x ) = x^2 + 2 x + 2`

`f(0) = 0^2 + 2(0) + 2=2`

`f(2) = 2^2 + 2(2) + 2=10`

`Average =(10-2)/(2-0)` = 4

Average rate of change is 4