Question

What is the average rate of change of the function over the interval x = 0 to x = 8?

Answer 1

I think the reason that guy got the answer wrong was because you wrote the problem as:

f(x)=2x−13x+5

instead of:

f(x)=2x−1/3x+5

Answer 2

To find the average rate of change, use the following formula:

$\frac{f(b) - f(a)}{b-a}$

a and b represent the values of the interval:

$a = 0, b = 8$

Simplify the original equation by combining like terms:

$2x - 13x = -11x$
$f(x) = -11x + 5$

Plug the interval values into the f(x) equation:

$f(0) = -11(0) + 5 = 0 + 5 = 5$
$f(8) = -11(8) + 5 = -88 + 5 = -83$

Plug in these values into the average rate of change formula:

$\frac{-83 - 5}{8 - 0} = \frac{-88}{8} = -11$

The average rate of change over this interval is -11.