Question

Given the function g(x) = x^2 – 10x + 19, determine the average rate of change of

the function over the interval 3 < x < 6.

Answer 1

- 1

Explanation:

The average rate of change of g(x) in the close interval [ a, b ] is

`(g(b)-g(a))/(b-a)`

Here [ a, b ] = [ 3, 6 ] , then

g(b) = g(6) = 6² - 10(6) + 19 = 36 - 60 + 19 = - 5

g(a) = g(3) = 3² - 10(3) + 19 = 9 - 30 + 19 = - 2

average rate of change =
`(-5-(-2))/(6-3)` =
`(-5+2)/(3)` =
`(-3)/(3)` = - 1