Question

F(x)=x 3−9xf, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x What is the average rate of change of f over the interval [2,6] open bracket, 12, comma, 6, close bracket?

Answer 1

`A(x) = 243`

Explanation:

Given

`f(x) = x^3 - 9x`

`Interval: (12,6)`

Required

Determine the average rate of change

Average rate is calculated as thus;

`A(x) = (f(b) - f(a))/(b - a)`

In this case; b = 12 and a = 6

Calculating f(12)

`f(12) = 12^3 - 9 * 12`

`f(12) = 1728 - 108`

`f(12) = 1620`

Calculating f(6)

`f(6) = 6^3 - 9 * 6`

`f(6) = 216 - 54`

`f(6) = 162`

Substitute 12 for b and 6 for a in
`A(x) = (f(b) - f(a))/(b - a)`

`A(x) = (f(12) - f(6))/(12 - 6)`

Substitute values for f(6) and f(12)

`A(x) = (1620 - 162)/(12 - 6)`

`A(x) = (1458)/( 6)`

`A(x) = 243`