find the average rate of change on the indicated intervals f(x) = x^3 - 2x ; [0,4]
To find the average rate of change on the interval [0,4] for the function f(x) = x^3 - 2x, we can follow these steps:
1. Calculate the value of f(x) at the two endpoints of the interval: f(0) and f(4).
- f(0) = (0)^3 - 2(0) = 0
- f(4) = (4)^3 - 2(4) = 64 - 8 = 56
2. Find the difference in function values: f(4) - f(0).
- 56 - 0 = 56
3. Determine the difference in x-values: 4 - 0.
- 4 - 0 = 4
4. Divide the difference in function values by the difference in x-values to find the average rate of change.
- Average rate of change = (f(4) - f(0)) / (4 - 0)
- Average rate of change = 56 / 4
- Average rate of change = 14
Therefore, the average rate of change on the interval [0,4] for the function f(x) = x^3 - 2x is 14.