Question

Given f(x)=17-x2, what is the average rate of change in f(x) over the interval [1, 5]?

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 ] = [ 1, 5 ]

f(b) = f(5) = 17 - 5² = - 8

f(a) = f(1) = 17 - 1² = 16

average rate of change =
`(-8-16)/(5-1)` =
`(-24)/(4)` = - 6