Find the average rate of change

f(x)=x^3-8x+9 a. from -3 to -2
b. from -1 to 5
c. from 5 to 9

A. what is average rate of change of f(x)=x^3-8x+9 from -3 to -2?

B. what is the average rate of change of f(x)-x^3-8x+9 from -1 to 5?

C. what is the average rate of change of f(x)=x^3-8x+9 from 5 to 9?

Please show work

How about if someone shows you how to do one and you do the rest?

The average of f'(x) over an interval a to b is the area under the f'(x) curve, divided by (b - a).

That equals f(b) - f(a), because the area under f'(x) dx is the integral, f(x)

A. f(-2) - f(-3) = -8 +16 +9
-(-27) -24 -9 = ?

a. is the answer -6

That is not what I get adding the numbers I gave you, but maybe I made a mistake.

I get +11

To find the average rate of change, we need to calculate the difference in the function values at the two given points and divide it by the difference in the corresponding x-values.

A. To find the average rate of change of f(x) = x^3 - 8x + 9 from -3 to -2, we need to calculate the difference between f(-2) and f(-3) and divide it by the difference between -2 and -3.

1. Substitute the values of -2 and -3 into the function:
f(-2) = (-2)^3 - 8(-2) + 9 = 8 + 16 + 9 = 33
f(-3) = (-3)^3 - 8(-3) + 9 = -27 + 24 + 9 = 6

2. Calculate the difference in the function values:
f(-2) - f(-3) = 33 - 6 = 27

3. Calculate the difference in the x-values:
-2 - (-3) = -2 + 3 = 1

4. Divide the difference in function values by the difference in x-values to find the average rate of change:
Average rate of change = (f(-2) - f(-3)) / (-2 - (-3)) = 27 / 1 = 27

Therefore, the average rate of change of f(x) = x^3 - 8x + 9 from -3 to -2 is 27.

B. To find the average rate of change of f(x) = x^3 - 8x + 9 from -1 to 5, we use the same process as above:

1. Substitute the values of -1 and 5 into the function:
f(-1) = (-1)^3 - 8(-1) + 9 = -1 + 8 + 9 = 16
f(5) = (5)^3 - 8(5) + 9 = 125 - 40 + 9 = 94

2. Calculate the difference in the function values:
f(5) - f(-1) = 94 - 16 = 78

3. Calculate the difference in the x-values:
5 - (-1) = 5 + 1 = 6

4. Divide the difference in function values by the difference in x-values to find the average rate of change:
Average rate of change = (f(5) - f(-1)) / (5 - (-1)) = 78 / 6 = 13

Therefore, the average rate of change of f(x) = x^3 - 8x + 9 from -1 to 5 is 13.

C. To find the average rate of change of f(x) = x^3 - 8x + 9 from 5 to 9, we again follow the same steps:

1. Substitute the values of 5 and 9 into the function:
f(5) = (5)^3 - 8(5) + 9 = 125 - 40 + 9 = 94
f(9) = (9)^3 - 8(9) + 9 = 729 - 72 + 9 = 666

2. Calculate the difference in the function values:
f(9) - f(5) = 666 - 94 = 572

3. Calculate the difference in the x-values:
9 - 5 = 4

4. Divide the difference in function values by the difference in x-values to find the average rate of change:
Average rate of change = (f(9) - f(5)) / (9 - 5) = 572 / 4 = 143

Therefore, the average rate of change of f(x) = x^3 - 8x + 9 from 5 to 9 is 143.