The idea of smoothing a function is an important concept in signal processing. If f is a function and dx is a small number, then the smoothed version of f is the function whose value at a point x is the average of f(x - dx), f(x), and f(x + dx).
Write a function smooth that takes two inputs, a function that computes f and a smoothing parameter dx, and returns a function that computes the smoothed value of f. Your function smooth should permit the following usage: