[Recall that elsewhere on the test, we defined the average value of an integrable function f on [a, b] to be .]

Prove that if f is a continuous function on [a, b] where a, b Î Â, b > a, then there exists at least one value x₀ Î (a, b) such that f (x₀) is the average value of f on [a, b]. Provide a reason for each line in your proof. (For example, if the reason is FTC, simply say, "by FTC.")