Author: Ryan Samaro 514

The average value of a function f(x) from a to b is defined as the integral of the function from a to b divided by the difference of a and b. I have defined the average value function, g(x), of a given function f(x) as the integral of f(t) from 0 to x divided by x. Now if we want to go backwards and find out what function, f(x), would have to be averaged to get g(x) we simply have to take the derivative of x*g(x). This process of Anti-Averaging could be completed infinitely many times. So, if we were to do it r times then what would the coefficient on the x^c term of the resulting function?