2. The given figure shows the graph of f'. a. State the intervals of x for which f is increasing. Why? ( 3, 6 ) fi( x ) is pos. b. State the intervals of x for which f is decreasing. Why? ( 0, 3. ) u ( 6, 8 ) is neg. . .. ... c. Find all values of x for which f assumes relative extrema. W . .. State what type and why. . . . N * = 3, 6 fi ( x ) = 0 and changes 1 1 . . . . .......... ..... ... signs. d.State the intervals of x for which fis concave up. Why? ( 6, 1) 4 (2, 4. 5)u (7, 8 ) WNLO .:.. f " ( x ) > 0 1 . . . . . . .. . .. . - . . . e. State the intervals of x for which fis concave down. Why? ( 1, 2 ) 4 ( 4. 5, 7 ) -4 2 3 4 S 6 7 8 f " ( x ) LO Graph of f' f. State the value(s) of x for which f assumes a point of k. State the intervals of x for which Inflection. Why? f"(x) is negative. Why? X = 1,2, 4.5, 7 f" ( x ) = 0 1. State the x value(s) for which f(x) has horizontal tangents. Why? A& Given f(2) =5, write the equation of the tangent line to to the graph of f at the point (2,5) y = ax + b Slope = 2 5 = 2 ( 2 ) +b y = 2x+1 5= 4+ b 1 = 60 h. Estimate the value of f"(4) i. State the x value(s) for which f"(x) is zero. Why? j. State the intervals of x for which the graph off"(x) is above the x-axis. Why