,

The average rate of change of a function can be found by calculating the change in values of the two points divided by the change in values of the two points.

Substitute the equation for and , replacing in the function with the corresponding value.

Simplify the numerator.

Raise to the power of .

Raise to the power of .

Multiply by .

Multiply by .

Simplify each term.

Raise to the power of .

Raise to the power of .

Multiply by .

Multiply by .

Subtract from .

Subtract from .

Add and .

Multiply by .

Subtract from .

Add and .

Add and .

Add and .

Simplify the denominator.

Multiply by .

Add and .

Divide by .

Find the Average Rate of Change f(x)=x^3-12x^2+21x+14 , [-1,9]