Question 10
What is the average rate of change of
f(x)=x2−x+4
from x=2 to x=4 ?
To find the average rate of change of a function, we need to calculate the difference in the function values divided by the difference in the input values.
First, let's find the function values at x=2 and x=4:
f(2) = (2)^2 - 2 + 4 = 4 - 2 + 4 = 6
f(4) = (4)^2 - 4 + 4 = 16 - 4 + 4 = 16
Next, let's calculate the difference in the function values:
f(4) - f(2) = 16 - 6 = 10
Finally, let's calculate the difference in the input values:
4 - 2 = 2
Now, we can determine the average rate of change:
Average rate of change = difference in function values / difference in input values
Average rate of change = 10 / 2
Average rate of change = 5
Therefore, the average rate of change of f(x)=x^2-x+4 from x=2 to x=4 is 5.
To find the average rate of change of a function from one point to another, we need to calculate the difference in function values divided by the difference in input values.
Given the function f(x) = x^2 - x + 4, we want to find the average rate of change from x = 2 to x = 4.
First, let's find the function value at x = 2:
f(2) = (2)^2 - 2 + 4
= 4 - 2 + 4
= 6
Now, let's find the function value at x = 4:
f(4) = (4)^2 - 4 + 4
= 16 - 4 + 4
= 16
The difference in function values is: 16 - 6 = 10.
Next, let's calculate the difference in input values: 4 - 2 = 2.
Finally, we can calculate the average rate of change:
Average rate of change = (difference in function values) / (difference in input values)
= 10 / 2
= 5
Therefore, the average rate of change of f(x) from x = 2 to x = 4 is 5.
To find the average rate of change of a function from one point to another, we need to calculate the difference in function values divided by the difference in input values.
In this case, we are given the function f(x) = x^2 - x + 4 and two points x=2 and x=4. We need to evaluate the function at these two points and find the difference in function values and input values.
Step 1: Evaluate the function at x=2.
Plugging in x=2 into the function f(x) = x^2 - x + 4, we get:
f(2) = 2^2 - 2 + 4 = 4 - 2 + 4 = 6.
Step 2: Evaluate the function at x=4.
Plugging in x=4 into the function f(x) = x^2 - x + 4, we get:
f(4) = 4^2 - 4 + 4 = 16 - 4 + 4 = 16.
Step 3: Calculate the average rate of change.
To find the average rate of change, we divide the difference in function values by the difference in input values:
Average rate of change = (f(4) - f(2)) / (4 - 2).
Substituting the values we calculated:
Average rate of change = (16 - 6) / (4 - 2) = 10 / 2 = 5.
Therefore, the average rate of change of the function f(x) from x=2 to x=4 is 5.