1. (28 points) CURVE SKETCHING. Given the function f(x) = x4 -2x2 -4 1. (2 points) Find f (x) and f"(x). 2. (16 points) Determine the following properties of the graph of f. a. Range and domain b. x and y intercepts C. The asymptotes d. The critical points e. The intervals on which f is increasing or decreasing f. The relative extrema pines g. The intervals on which f is concave up or concave down h. The Inflection points 3. (5 points) Create a table for graphing using the information obtained from (1 and 2). 4. (5 points) Sketch the graph of f using the table you created. Il. (10 points) MEAN VALUE THEOREM Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval and find all values of c in that interval that satisfy the conclusion of the theorem. $1 /() =x'-x on [0,2] Ill. (10 points) OPTIMIZATION A rectangular page is to contain 30 square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used. IV. (20 points) INDETERMINATE FORMS Show if the following limits produce an indeterminate form. Then, evaluate the following limits. 1. (10 points) lim In (x) X-+00 Vx 2. (10 points) lim x2-2x+1 where a and b are nonzero constants x-+1 4x2-2x+1