Question

Given the function g(x) = x2 + 6x + 2, determine the average rate of change of

the function over the interval -7 < < -2.

Answer 1

average rate of change = - 3

Explanation:

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

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

here [ a, b ] = [ - 7, - 2 ] , then

f(b) = f(- 2) = (- 2)² + 6(- 2) + 2 = 4 - 12 + 2 = - 6

f(a) = f(- 7) = (- 7)² + 6(- 7) + 2 = 49 - 42 + 2 = 9

Then

average rate of change =
`(-6-9)/(-2-(-7))` =
`(-15)/(-2+7)` =
`(-15)/(5)` = - 3