6. Let f(x) = 33:\"3 x . Use non- graphical methods to nd the answer to each of the following. (3) Determine the interva1(s) of increase and decrease for f (x) . (b) Find all x-values where f (x) has a local maximum or local minimum. Classify each x-value accordingly. (c) Find the intervals of concavity and any inection points. (d) Using the information gathered in parts (a), (b), and (c), sketch a graph of f (x) below including all intercepts. Also, plot several points on the graph. Section 4.114.314.4 Activity Shapes of Graphs 1. In general, what are the critical numbers of a function f (x) ? 2. True or False? Explain: If x = c is a critical number of a function f (x) , then (c, f(c)) is either a local maximum point or a local minimum point for f (x) . 3. Find the critical numbers for each of the following function: f (x) = x\"3 x.\"3 4. Find the absolute minimum and absolute maximum values of g(x) =1n(x2 + x+1) on the interval [1, 1] . 7. Let f(x) be a function which has each and every one of the following conditions. Draw an accurate graph of f (x) in the plane below. (a) lim f(x) = 3 (b) lim f (x) =1 (c) lim f(x) = 00 (d) lim f(x) = -0o (e) f'(x) > 0 on (-1, 2) (4, 5) (5, 00) (f) f'(x) 0 on (-3, 1) U (3, 5) (i) f"(x)