Question

Let f(x)=x^2+5x-8. What is the average rate of change from x = 2 to x = 6? Enter the answer in the box ___

please show the work and answer

Answer 1

13

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 ]

f(b) = f(6) = 6² + 5(6) - 8 = 36 + 30 - 8 = 58

f(a) = f(2) = 2² + 5(2) - 8 = 4 + 10 - 8 = 6

Hence

average rate of change =
`(58-6)/(6-2)` =
`(52)/(4)` = 13