Find the average rate of change of f(x) 3x^2-4x from x=3 to x=6 .

Simplify your answer as much as possible.

f(6) = 84

f(3) = 15
----------
f(6)-f(3)=69

69/(6-3) = 23

Well, let's start by finding the value of f(x) at x=3 and x=6.

At x=3, we have f(3) = 3(3)^2 - 4(3) = 27 - 12 = 15.
At x=6, we have f(6) = 3(6)^2 - 4(6) = 108 - 24 = 84.

Now, let's find the average rate of change. It is given by the formula:

Average rate of change = (f(6) - f(3)) / (6 - 3)

Substituting the values we found, we get:

Average rate of change = (84 - 15) / (6 - 3) = 69 / 3 = 23.

So, the average rate of change of f(x) from x=3 to x=6 is 23.

To find the average rate of change of a function from x = 3 to x = 6, we need to calculate the difference in the function values at those two points and divide it by the difference in x-values.

First, let's find the value of f(x) at x = 3:
f(3) = 3(3)^2 - 4(3)
= 3(9) - 12
= 27 - 12
= 15

Next, let's find the value of f(x) at x = 6:
f(6) = 3(6)^2 - 4(6)
= 3(36) - 24
= 108 - 24
= 84

Now, let's calculate the difference in the function values:
f(6) - f(3) = 84 - 15
= 69

Lastly, let's calculate the difference in x-values:
6 - 3 = 3

Therefore, the average rate of change of f(x) from x = 3 to x = 6 is:
( f(6) - f(3) ) / ( 6 - 3 )
= 69 / 3
= 23

So, the average rate of change of f(x) from x = 3 to x = 6 is 23.

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

First, let's find the value of f(x) when x = 3:
f(3) = 3(3)^2 - 4(3) = 3(9) - 12 = 27 - 12 = 15.

Next, let's find the value of f(x) when x = 6:
f(6) = 3(6)^2 - 4(6) = 3(36) - 24 = 108 - 24 = 84.

The difference in the values of f(x) is:
84 - 15 = 69.

The difference in the x-values is:
6 - 3 = 3.

Therefore, the average rate of change of f(x) from x = 3 to x = 6 is:
(69) / (3) = 23.

So, the average rate of change is 23.