1. (10 points) Sketch the graph of a function that satisfies all the conditions: f is continuous everywhere except at r = 4 lim f(x) = 1 lim f(x) = -co I-+00 r-4+ f has absolute maximum at r = 4, f is not differentiable at x = 2, f'(x) > 0, if 2 4, and f'(x) 4. 2. (12 points) Consider the function f(x) = x - 3x on the closed interval [-1, 1] a. Verify that f(x) satisfies the hypothesis of Rolle's Theorem