The function f(x) = 3x2 - 4x + 2 can be used to determine the position of a turtle, f(x), in inches, after x seconds. Find the average rate of change of the function, in inches per second, over the interval [1, 5].
A.
42
B.
16
C.
14
D.
56
To find the average rate of change of the function over the interval [1, 5], we need to find the difference in the function values at the endpoints of the interval and divide by the difference in the x-values.
First, let's find f(1) and f(5).
f(1) = 3(1)^2 - 4(1) + 2 = 3 - 4 + 2 = 1
f(5) = 3(5)^2 - 4(5) + 2 = 75 - 20 + 2 = 57
Next, let's find the difference in the function values: f(5) - f(1) = 57 - 1 = 56
Finally, let's find the difference in the x-values: 5 - 1 = 4
The average rate of change of the function over the interval [1, 5] is given by the formula (f(5) - f(1))/(5 - 1) = 56/4 = 14
So the average rate of change of the function, in inches per second, over the interval [1, 5] is 14. Therefore, the answer is C. 14.
To find the average rate of change of the function f(x) = 3x^2 - 4x + 2 over the interval [1, 5], we need to calculate the difference in the function values at the endpoints of the interval and divide it by the difference in the x-values.
Step 1: Calculate the value of f(1):
f(1) = 3(1)^2 - 4(1) + 2
f(1) = 3 - 4 + 2
f(1) = 1
Step 2: Calculate the value of f(5):
f(5) = 3(5)^2 - 4(5) + 2
f(5) = 75 - 20 + 2
f(5) = 57
Step 3: Calculate the difference in the function values:
Δf = f(5) - f(1)
Δf = 57 - 1
Δf = 56
Step 4: Calculate the difference in x-values:
Δx = 5 - 1
Δx = 4
Step 5: Calculate the average rate of change:
Average Rate of Change = Δf/Δx
Average Rate of Change = 56/4
Average Rate of Change = 14
Therefore, the average rate of change of the function over the interval [1, 5] is 14 inches per second.
So, the correct answer is C. 14.
To find the average rate of change of the function over the interval [1, 5], we need to calculate the difference in the function values at the endpoints of the interval and divide by the difference in x-values.
First, calculate the value of f(x) at x=1:
f(1) = 3(1)^2 - 4(1) + 2 = 3 - 4 + 2 = 1
Next, calculate the value of f(x) at x=5:
f(5) = 3(5)^2 - 4(5) + 2 = 75 - 20 + 2 = 57
Now, calculate the difference in the function values:
f(5) - f(1) = 57 - 1 = 56
Finally, calculate the difference in x-values:
5 - 1 = 4
To find the average rate of change, divide the difference in function values by the difference in x-values:
Average rate of change = (f(5) - f(1)) / (5 - 1) = 56 / 4 = 14
Therefore, the average rate of change of the function over the interval [1, 5] is 14 inches per second.
The correct answer is C. 14.