Question

Calculate the average rate of change of f(x) = x2 - 1 x - 3 for 1 ≤ x ≤ 3. A) - 13 3 B) - 3 13 C) 13 3 D) 3 13

Answer 1

`Answer: \\ f(1) = - 3 \\ f(3) = 3 \\ Average \: rate \: of \: change: \\ (f(3) - f(1))/(3 - 1) = (6)/(2) = 3`

Answer 2

3

Explanation:

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

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

here [ a, b ] = [ 1, 3 ]

f(b) = f(3) = 3² - 3 - 3 = 9 - 3 - 3 = 3

f(a) = f(1) = 1² - 1 - 3 = 1 - 1 - 3 = - 3

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