Question

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

f(x)=2x−13x+5

Enter your answer, as a fraction, in the box.

Answer 1

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


`(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:


`(-83 - 5)/(8 - 0) = (-88)/(8) = -11`

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