Question

What is the average rate of change for the function f(x)=3x^2 -5 on the interval −3 ≤ x ≤ −1 ?

Answer 1

-12

Explanation:

Let b = -1 and a = -3

The average rate of change =
`(f(b) - f(a))/(b - a)`

f(b) = f(-1) = 3(-1)^2 - 5 = 3 - 5 = -2

f(a) = f(-3) = 3(-3)^2 - 5 =27 - 5 = 22

f(b) - f(a) = -2 - 22 = -24

b - a = -1 + 3 = 2

`(f(b) - f(a))/(b - a)` = -24/2 = -12