Question

Find the average rate of change of f(x)=-x^2+2x+2 from x=2 to x=6. Simplify your answer as much as possible.

Answer 1

- 6

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 ] = [ 2, 6 ] , then

f(b) = f(6) = - 6² + 2(6) + 2 = - 36 + 12 + 2 = - 22

f(a) = f(2) = - 2² + 2(2) + 2 = - 4 + 4 + 2 = 2 , then

average rate of change =
`(-22-2)/(6-2)` =
`(-24)/(4)` = - 6