Question

For each problem, find the average rate of change of the function over the given interval.3. F(x) = 2x - 4x + 9, [0,9)4. (-2,21

Answer 1

You have the following function:

`f(x)=2x^2-4x+9`

Take into account that the average rate of change is given by the following formula:

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

where x1 and x2 are the limits of a given interval.

In this case, you have x1 = 0 and x2 = 9. Replace these values to calculate f(0) and f(9):

`\begin{gathered} f(0)=2(0)^2-4(0)+9=9 \\ f(9)=2(9)^2-4(9)+9=2(81)-36+9=162-36+9=135 \end{gathered}`

Next, replace the previous results into the formula for m:

`m=(135-9)/(9-0)=(126)/(9)=14`

Hence, the average rate of change is 14