Show that the circumference of every circle of radius R is 27R by finding the arc length of an appropriate function on an appropriate interval and then exploiting the symmetry of a circle. Given f(x) = x", where n is any positive integer, and a bounded interval [a, b], find c in the open interval (a, b) such that f (c) is equal to f (recall from class this is the notation we will use for the average value of f on [a, b]). hint: it may help to investigate the situation for small values of n, such as 1, 2, 3