1. Let f(x) = 4x5 + 5x3 - 5x with f'(x) = 5(2x - 1)(2x + 1)(x2 + 1) and f"(x) = 10x(8x2 + 3). (a) Use the Mean Value Theorem to show that there exists a point on f in [0, 1] whose tangent line has a slope of 4. (b) Find the intervals where f is increasing or decreasing, concave up or concave down. (c) Determine the relative extremum points and points of inflection of f. 2. Let x+2 1 - x g(x) = 23 +x2 -4 x2 - 1 The function g is concave up on (-oo, 1), concave down on (1, +oo), and increasing on both (-oo, 1) and (1, too). Use limits to identify all linear asymptotes of g and sketch the graph of g