1. Consider the following two functions:

f(x) = x4 - 2x3 - 5x2 + 6x - 2 and g(x) = -(x + 2)e-x.

a. Find the derivative of each of these functions.

b. Find the x and y-intercepts for each of these functions. Determine all extrema (minima and maxima) for f(x) and g(x). If there are any asymptotes, then state where they are. Plot the graphs of these functions on the interval -4 < x < 4.

c. Find the x and y values for all points of intersection between f(x) and g(x). (There are 5 of them, not necessarily in the interval you graphed.)