Final answer:
To find the average rate of change of the function f(x) = x² - 8x + 22 on the interval [3, t], substitute the x-values 3 and t into the function and calculate their corresponding function values. Then, calculate the average rate of change by dividing the change in the function value by the change in x-values.
Step-by-step explanation:
To find the average rate of change of the function f(x) = x² - 8x + 22 on the interval [3, t], we need to calculate the change in the function value divided by the change in x-values. Let's substitute the x-values 3 and t into the function and calculate the corresponding function values. Then we can calculate the average rate of change.
Using the given function, f(3) = (3)² - 8(3) + 22 = 11 and f(t) = t² - 8t + 22. The average rate of change on the interval [3, t] is:
Average rate of change = (f(t) - f(3)) / (t - 3) = (t² - 8t + 22 - 11) / (t - 3) = (t² - 8t + 11) / (t - 3).