1. If f(x) = x' -6x , then f (x) has a local minimum at a. x =-2 b. x=0 c. x=-V2 d. x=2 e. x=V2 2. If f'(x) = (x+3)(x-2)?(x-4) , then f(x) has (a) a local minimum at x = 2 (b) a local maximum at x = 4 (c) both a local minimum at x = 2 and a local maximum at x = -3 (d) neither a local minimum nor a local maximum (e) both a local minimum at x = 4 and a local maximum at x =-3 3. How many inflection points does the function f (x) = x2 (x -1) have? 1 b . 4 c. 5 d. 6 e. none 4. Find the interval on which f(x) = xe * is increasing. a. (-00, 1] b. (-00, 2] c. (-00, 3] d. [1,2] e. (-oo, e] 5. True or False (14pts) a. There is a local maximum or local minimum at each critical number. b. If f"(x) 0 for all values of x, then f(x) concave up. If f"(2) =0, then the graph of f (x) must have a point of inflection at x = 2. e . If f'(x) =0 or f'(x) is undefined and c is in the domain of f (x) , then c is a critical point of f (x) . f. S ( Inx) dx =+c g