Final answer:
The average rate of change of a function over an interval is defined as the change in the y-values divided by the change in the x-values. To find the average rate of change of function f over the interval [2,6], we need to calculate the difference in the f(x) values at x=6 and x=2, and then divide it by the difference in x values, which is 6-2=4.
Step-by-step explanation:
The average rate of change of a function over an interval is defined as the change in the y-values divided by the change in the x-values. To find the average rate of change of function f over the interval [2,6], we need to calculate the difference in the f(x) values at x=6 and x=2, and then divide it by the difference in x values, which is 6-2=4.
Let's say the function f(x) = 3x^2 - 2x + 1. To find the average rate of change of f over the interval [2,6], we evaluate f(6) and f(2), and then calculate (f(6) - f(2))/(6-2).
For example, if f(x) = 3x^2 - 2x + 1, then f(6) = 3(6)^2 - 2(6) + 1 = 109 and f(2) = 3(2)^2 - 2(2) + 1 = 11. So the average rate of change of f over the interval [2,6] is (109 - 11)/(6-2) = 98/4 = 24.5.