AP Calculus Chapter 5.1-5.9 AB Name: 1. The graph of f(x), the derivative of a function f(x), is pictured below on the closed interval [-10, 10]. f'(x) had relative extreme values at x = -3, x = 2, and x = 6. Use the graph to answer the following questions. f'(x) -10-9-8/-7-6-5-4-5-2-10 a. On what interval(s) of x is the graph f (x) decreasing? Justify your reasoning. b. At what values of x does the graph of f (x) have an inflection point? Justify the reasoning. 2. If f'(x) = x(x+1)(x-2)2, determine which of the following are correct statements. I. f (x) has a relative maximum at x = -1 II. f (x) has a relative minimum at x = 2 III. f (x) is increasing over the interval (-1,0) and (2, 0o ) a. I b. I and II c. I and III d. II and III e. I, II and III 3. The function f(x) is given by f(x) = x4+ 4x3 - 20x2 - 2. On which of the following intervals is f (x) decreasing? (a ) (2,00 ) ( b) ( - 5, 0) ( 2 , 00 ) ( c ) ( - 00 , - 5 ) ( 2 , 00 ) ( d ) ( - 00 , - 5 ) ( 0 , 2 )