Question

F(x)=x^3-9x
What is the average rate of change of f over the interval (1,6]?

Answer 1

34

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, 6 ]

f(b) = f(6) = 6³ - 9(6) = 216 - 54 = 162

f(a) = f(1) = 1³ - 9(1) = 1 - 9 = - 8, thus

average rate of change =
`(162-(-8))/(6-1)` =
`(170)/(5)` = 34