CHAPTER 4 Graphing and Optimis 16. 270 29. f(x) = 1+ x+x2/5 30. f(x) = x3/5 - 6x + 7 B In Problems 31-40, find the intervals on which the graph of fis concave upward, the intervals on which the graph off is concave downward, and the x, y coordinates of the inflection points. 31. f(x) = x4 -24x2 32. f(x) = 3x4 - 18x2 33. f(x) = x3 - 3x2 + 7x + 2 47. 34. f(x) = -x3 + 3x2 + 5x- 4 f(x ) - 4 35. f(x) = -x4+12x3 - 7x + 10 36. f(x) = x4 - 2x3 - 5x + 3 1() + + ND 1 37. f (x) = In (x2 + 4x + 5) 38. f(x) = In (x2- 4x + 5) 39. f(x) = 403x - 9e2x 40. f(x) = 16el - gett In problems 41-44, use the given sign chart to sketch a possible graph off. 41. f' ( x ) + + + + + + 0 - 0+ + + + + + 48. X -. N f ( x ) 42. f' (x ) 0 + + + ++++++0-- 0 43. f" ( x ) + + + + + ND + + ++ +++ + + + " N 44. : f" (x ) 49. f(0) = 2, f(1) ND + + + +++++ f' (0) = 0,/' (2) f' (x) > 0 08 ( In Problems 45-52, f(x) is continuous on ( -co, co ) . Use the given information to sketch the graph of f. f' (x) Don ( 1.5 0Intervals (-00, - 1) (-1, 1/2) (1/2, 00) Test Value F"(TV) Sign of f"' (test value) Concave up/Concave down