1. Given f(x) = 1/(x^2 + 1), do the following: (a) Use the quotient rule to find f'(x) and f''(x). In each case, simplify as much as possible. (b) Find the critical numbers of f(x), that is, where f'(x) = 0 or f'(x) does not exist. (c) Use test points and a sign chart to determine where f(x) is increasing, decreasing, and whether it has any local extrema. (d) Find the critical numbers of f'(x), that is, where f''(x) = 0 or f''(x) does not exist. (e) Use test points and a sign chart to determine where f(x) is concave up, concave down, and whether it has any inflection points. (f) Use a limit at infinity to determine whether f(x) has a horizontal asymptote. (g) Draw an accurate sketch of the graph of y = f(x). Be sure to label any local extrema and inflection points.