Question

How would you solve this?

Answer 1

average rate of change =
`(1)/(2)`

Explanation:

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

`(h(b)-h(a))/(b-a)`

here the interval is - 2 ≤ x ≤ 2 , then

h(b) = f(2) =
`(1)/(8)` (2)³ - 2² =
`(1)/(8)` (8) - 4 = 1 - 4 = - 3

h(a) = h(- 2) =
`(1)/(8)` (- 2)³ - (- 2)² =
`(1)/(8)` (- 8) - 4 = - 1 - 4 = - 5

then average rate of change

=
`(-3-(-5))/(2-(-2))`

=
`(-3+5)/(2+2)`

=
`(2)/(4)`

=
`(1)/(2)`