What is the average rate of change of the function f(x) on the interval −6 ≤ x ≤4?
(f(4) - f(-6)) / (4-(-6))
To find the average rate of change of a function on an interval, you can use the formula:
Average Rate of Change = (f(b) - f(a))/(b - a)
In this case, the interval given is -6 ≤ x ≤ 4, so a = -6 and b = 4. Let's denote f(x) as y for simplicity. To calculate the average rate of change of the function f(x) on this interval, we need to evaluate f(4) and f(-6) and substitute them in the formula.
So, the average rate of change of the function f(x) on the interval -6 ≤ x ≤ 4 is:
Average Rate of Change = (f(4) - f(-6))/(4 - (-6))
To find the average rate of change of a function on an interval, you need to calculate the difference in the function value divided by the difference in the input variables within that interval.
In this case, you are given the function f(x) and the interval −6 ≤ x ≤ 4. To find the average rate of change, follow these steps:
1. Determine the function values at the endpoints of the interval. Calculate f(−6) and f(4) using the given function f(x).
2. Compute the difference in the function values, f(4) − f(−6).
3. Calculate the difference in the input variables, 4 − (−6).
4. Divide the difference in the function values by the difference in the input variables to get the average rate of change.
Here's the formula for the average rate of change:
Average Rate of Change = (f(4) - f(-6)) / (4 - (-6))
Compute the function values using the given function f(x) and then apply the formula to find the average rate of change.