1. Let f(x) = xi . (x - 4). Give exact answers to the following questions. (a) Find the vertical or horizontal asymptotes of f, if any. (b) Find the intervals of increase and decrease of f and determine if f has any local extrema. Are these local extrema absolute? (c) Find the intervals of concavity of f and determine if f has any inflection points. 2. Repeat #1 for the function f (x) = e* (x] - 3). 3. Determine the absolute extreme values of f on the given interval: f (x) = 2x-x on [0,2] 4. For what values of c does the polynomial P(x) = x* + cx3 + x have no inflection points? 5. Sketch the graph of a function h(x) satisfying the following conditions. h'(x) > 0 if |x] 2 h"(x) 0ifx>3 h'(2) = 0 lim h(x) = 1 h(-x) = -h(x) 6. A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is (a) a maximum? (b) a minimum? Be sure to prove your answer is absolute.7. Evaluate each limit. (a) If f is continuous and f(2) = 0 and f'(2) = 7 then evaluate lim ! /(2+5x)+/ (2+7x) (b) lim - where n is a positive integer rix-1 8. True or False: If the statement is true, prove or explain why. If the statement is false, give a counterexample that disproves the statement. (a) If f is differentiable and f(-1) = f(1) then there is a number c such that |cl