F(x)= x^3 - 9xf(x)=x 3 −9xf, left parenthesis, x, right parenthesis, equals, x, cubed, minus, 9, x What is the average rate of change of fff over the interval [-1,2][-1,2]open bracket, 1, comma, 6, close bracket?

The average rate of change of over the interval is -6.

Step-by-step explanation:

The average rate of a function at a given interval is calculated by definition of secant line, whose slope is:

(Eq. 1)

Where:

- Lower bound, dimensionless.

- Upper bound, dimensionless.

- Function evaluated at lower bound, dimensionless.

- Function evaluated at upper bound, dimensionless.

If we know that , and , then the average rate of change of over the interval is:

Lower bound

Upper bound

Secant line

The average rate of change of over the interval is -6.