1. Sketch the graph of the function by collecting the following information. You must show all your work to receive full credit. Your sketch should match the information you provide in a-e, and no credit will be given for a correct graph with no supporting information. f(x) = x 4 x - 1 a. Domain and Range b. Intercepts: x-intercepts and y-intercepts c. Asymptotes: Vertical Asymptotes and Horizontal Asymptotes d. Increasing/Decreasing: Label what intervals are increasing and what intervals are decreasing. When finding the first derivative - show your work. Final answer should be in interval notation. Are there any local maxes/local mins? If so, where? e. Concavity: Label what intervals are concave up and what intervals are concave down. When finding the second derivative show your work. Final answer should be in interval notation. f. Graph 2. A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume?