Question

Find the average rate of change of f(x)=2x^2-2 from 2 to 4

Answer 1

average rate of change = 12

Explanation:

the average rate of change of f(x) in the interval a ≤ x ≤ b is

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

here the interval is 2 ≤ x ≤ 4 , then

f(b) = f(4) = 2(4)² - 2 = 2(16) - 2 = 32 - 2 = 30

f(a) = 2(2)² - 2 = 2(4) - 2 = 8 - 2 = 6

then

average rate of change =
`(30-6)/(4-2)` =
`(24)/(2)` = 12