Key Points:
- The formula calculates the average rate of change of a function over a given interval.
- The difference in function values (F(b) - F(a)) is divided by the difference in input values (b - a).
==Example 1:==
- Function: f(x) = 3x^2
- Interval: [1, 3] [a, b] a = 1, b = 3
- Average Rate of Change = (F(3) - F(1)) / (3 - 1)
- Substituting into the function: (27 - 3) / 2 = 24 / 2 = 12
In Example 1, ==the function f(x) = 3x^2== has an ==average rate of change of 12 over== the ==interval [1, 3].==
^^Example 2:^^
- Function: f(x) = x^2 + 2
- Interval: [2, 4] [a, b] a = 2, b = 4
- Average Rate of Change = (F(4) - F(2)) / (4 - 2)
- Substituting into the function: (18 - 6) / 2 = 12 / 2 = 6
In Example 2, ^^the function f(x) = x^2 + 2^^ has an ^^average rate of change of 6 over^^ the ^^interval [2, 4].^^
Conclusion:
- Overall, the Average rate of change provides insight into the trend of the function within the specified interval.