Question

Find the average rate of change of the function over the given interval. f(x) = 3x − 2; [0, 5]

Answer 1

The average rate of change of the function over the given interval is 3.

Step-by-step explanation:

To find the average rate of change of the function over the given interval, we need to calculate the change in the function values and divide it by the change in the input values.

Step 1: Calculate the function values for the two endpoints of the interval.

f(0) = 3(0) - 2 = -2

f(5) = 3(5) - 2 = 13

Step 2: Calculate the change in the function values.

Change in function values = f(5) - f(0) = 13 - (-2) = 15

Step 3: Calculate the change in the input values.

Change in input values = 5 - 0 = 5

Step 4: Divide the change in function values by the change in input values.

Average rate of change = (Change in function values) / (Change in input values) = 15 / 5 = 3

Answer 2

To find the avarage rate of change, we first need to find our y-coordinates.
This brings us to our first step: filling in the x-coordinates (of the domain) in the formula.

f(0) = 3*0 - 2 = -2
f(5) = 3*5 - 2 = 15- 2 = 13

We now have found the following coordinates
(0,-2) and (5,13).

To find the avarage rate of change we need to use the following formula:
rate of change = Δy / Δx
With Δ representing the change of coordinates. Filling in this formula, gives us:
rate of change =
`(13 - -2)/(5 - 0) = (15)/(5) = 3`

So our answer: the average rate of change on the interval (domain) [0,5] is 3.