Consider the following two functions:

f(x) = 2 - 4 cos(3x) and g(x) = 3 sin(x2 - 1).

a. Find the derivative of each of these functions using Maple. Write a brief description of your observations on the rules of differentiating these functions.

b. Graph the functions f(x) and g(x) on the interval -2p < x < 2p. Are these functions periodic, and if so, what is the period? These functions both oscillate. Find the largest and smallest y values that they oscillate between. Determine an x value for each of these functions where the function is at a maximum and at a minimum (only one of each as there are infinitely many). Also, find one x-intercept for each function.