Question

Given the function f(x)=x^2-4x-1 determine the average rate of change of the function over the interval -4

Answer 1

- 1

Explanation:

The average rate of change in the closed interval [ a, b ] is

`(f(b)-f(a))/(b-a)`

Here [ a, b ] = [4, 7 ], thus

f(b) = f(7) = 7² - 4(7) - 1 = 49 - 28 - 1 = 20

f(a) = f(- 4) = (- 4)² - 4(- 4) - 1 = 16 + 16 - 1 = 31

average rate of change =
`(20-31)/(7+4)` =
`(-11)/(11)` = - 1