What is the average rate of change for ƒ(x) = 2x + 10 over the interval 2 ≤ x ≤ 4?
(f(4)-f(2))/(4-2) = ____
or, since it is a linear function, just use the slope, which is the same everywhere.
Well, instead of giving you the average rate of change, how about I give you the average rate of clownification? It's much more fun!
Now, let's calculate how much clowniness ƒ(x) = 2x + 10 brings to the interval 2 ≤ x ≤ 4. We'll start by plugging in the values of x into the equation:
ƒ(2) = 2(2) + 10 = 4 + 10 = 14
ƒ(4) = 2(4) + 10 = 8 + 10 = 18
Now, let's find the change in clowniness (which is just a fancy way of saying the change in the function values):
Change in clowniness = ƒ(4) - ƒ(2) = 18 - 14 = 4
So, over the interval 2 ≤ x ≤ 4, the average rate of clownification (I mean, change) is 4. I hope that brings a smile to your face!
To find the average rate of change for ƒ(x) = 2x + 10 over the interval 2 ≤ x ≤ 4, we need to calculate the change in the function's values and divide it by the change in x.
Step 1: Find the value of ƒ(4):
Plug in the value x = 4 into the function:
ƒ(4) = 2(4) + 10 = 18
Step 2: Find the value of ƒ(2):
Plug in the value x = 2 into the function:
ƒ(2) = 2(2) + 10 = 14
Step 3: Calculate the change in ƒ(x):
Change in ƒ(x) = ƒ(4) - ƒ(2) = 18 - 14 = 4
Step 4: Calculate the change in x:
Change in x = 4 - 2 = 2
Step 5: Calculate the average rate of change:
Average rate of change = Change in ƒ(x) / Change in x = 4 / 2 = 2
Therefore, the average rate of change for ƒ(x) = 2x + 10 over the interval 2 ≤ x ≤ 4 is 2.
To find the average rate of change for a function over a given interval, we need to determine the change in the value of the function divided by the change in x over that interval.
For the function ƒ(x) = 2x + 10, we want to find the average rate of change over the interval 2 ≤ x ≤ 4. This means we need to find the change in ƒ(x) over this interval, as well as the change in x.
To find the change in ƒ(x), we evaluate the function at the upper and lower bounds of the interval and subtract the values. So, we find ƒ(4) - ƒ(2).
ƒ(4) = 2(4) + 10 = 8 + 10 = 18
ƒ(2) = 2(2) + 10 = 4 + 10 = 14
Therefore, the change in ƒ(x) over the interval is 18 - 14 = 4.
To find the change in x, we subtract the lower bound from the upper bound. In this case, it is 4 - 2 = 2.
Now, we can calculate the average rate of change by dividing the change in ƒ(x) by the change in x: 4 / 2 = 2.
So, the average rate of change for ƒ(x) = 2x + 10 over the interval 2 ≤ x ≤ 4 is 2.