Calculate the average rate of change over the given interval of the given function.

f (x) = x3, from x = 8 to x = 9

f(8) = 8^3 = 512

f(9) = 9^3 =729

averg rate of change = (729-512)/(9-8) = 217

To calculate the average rate of change of a function over a given interval, we need to find the difference in function values at the endpoints of the interval and divide it by the difference in x-values.

In this case, the function is f(x) = x^3 and the interval is from x=8 to x=9.

First, let's find the function values at the endpoints:
f(8) = 8^3 = 512
f(9) = 9^3 = 729

Next, let's calculate the difference in y-values:
Δy = f(9) - f(8) = 729 - 512 = 217

Finally, let's calculate the difference in x-values:
Δx = 9 - 8 = 1

Now, we can calculate the average rate of change:
Average rate of change = Δy / Δx = 217 / 1 = 217

Therefore, the average rate of change of the function f(x) = x^3 over the interval [8, 9] is 217.

To calculate the average rate of change of a function over a given interval, we need to find the change in the function's value divided by the change in the input value. In this case, we are given the function f(x) = x³ and the interval from x = 8 to x = 9.

First, let's find the change in the function's value by plugging in the values of x into the function:

f(8) = 8³ = 512
f(9) = 9³ = 729

Next, let's find the change in the input value:

change in x = 9 - 8 = 1

Now, we can calculate the average rate of change:

average rate of change = (change in f(x)) / (change in x)
= (729 - 512) / 1
= 217

Therefore, the average rate of change of the function f(x) = x³ from x = 8 to x = 9 is 217.