What's the avearage rate of change of f(x)=x^2-4x+7 on the interval 1<=x<=3
To find the average rate of change of a function on a given interval, you need to calculate the difference in the function values divided by the difference in the values of the independent variable. In this case, we are given the function f(x) = x^2 - 4x + 7 and the interval 1 ≤ x ≤ 3.
Step 1: Calculate the function values at the endpoints of the interval.
- At x = 1: f(1) = (1^2) - 4(1) + 7 = 1 - 4 + 7 = 4
- At x = 3: f(3) = (3^2) - 4(3) + 7 = 9 - 12 + 7 = 4
Step 2: Calculate the difference in the function values.
- Difference = f(3) - f(1) = 4 - 4 = 0
Step 3: Calculate the difference in the values of the independent variable.
- Difference = 3 - 1 = 2
Step 4: Calculate the average rate of change.
- Average rate of change = Difference in function values / Difference in independent variable values
- Average rate of change = 0 / 2 = 0
Therefore, the average rate of change of f(x) = x^2 - 4x + 7 on the interval 1 ≤ x ≤ 3 is 0.