SECTION 4.1 First Derivative and Graphs 253 (a f' ( ) o+ + + + + + + + 43 . f (x ) = *4 + 4x3 + 30 44. f (x ) = x4 - 8x3 + 32 45 . f (x ) = (x+ 3 ) ex 46. f ( x) = (x+ 2)ex 47 . f( x ) = (x2 - 4) 213 48. f(x ) = (x2 - 4) 1/3 (b ) f' () - ND + + + + + + + + In Problems 49-56, find the intervals on which f( x) is increasing and the intervals on which f(x) is decreasing. Then sketch the graph. Add horizontal tangent lines. (C) 49. f (x ) = 4+ 8x -x2 f( ) + + + + + + + + 0+ + ++ + + + + 50. f (x ) = 2x2 - 8x + 9 51. f (x ) = x3 - 3x + 1 (0) 10 = (S (d) 52. f (x ) = x3 - 12x + 2 f (x) + + + + + + + + ND+ + + + + + + + 53. f (x ) = 10-12x + 6x2 - x3 54. f(x) = x3 + 3x2 + 3x (e) f' ( x) + + + + + + + + 0 55 . f(x ) = x4 - 18x2 56. f (x ) = -x4+50x2 (f) In Problems 57-60, use a graphing calculator to approximate the f (x ) + + + + + + + + ND critical numbers of f(x) to two decimal places. Find the inter- vals on which f(x) is increasing, the intervals on which f( x) is decreasing, and the local extrema. g) 57. f(x) = x4 - 4x' + 9x 58. f (x ) = x4+ 5x3 - 15x f' (x) - ND 59 . f (x ) = ex - 3x2 60. f(x) = ex - 2x2 (h) In Problems 61-68, f(x) is continuous on ( -0o, co ). Use the f ( x) given information to sketch the graph off. 61. f'(x ) + + + 0+ + + 0 B In Problems 27-32, find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. 27. f ( x ) = 1 - 12x + 8 28. f ( x ) = x - 27x + 30 X - 2 - 1 1 2 6 5 f (x) - 1 1 2 3 29. f (x ) =- * + 2 30. f(x) = x - 4 62. 31. f(x) =x1/3 32. f(x ) =x2/3 f' (x) 0 In Problems 33-48, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. 33. f( x ) = 3x2 - 12x + 2 34. f(x) = 5x2 - 10x -3 -2 -1 0 1 2 35. f( x) = -2x2 - 16x - 25 f(x) 1 3 1 - 1 36. f(x) = - 3x2+ 12x - 5 63. 37. f(x ) = x3+ 5x+ 2 f' (x ) - 0+ + + ND 0 38. f ( x) = -x - 2x - 5 TO .... NO" 39. f ( x ) = x3 - 3x + 5 40. f( x ) = -x3 + 3x + 7 41. f(x) = -3x3 - 9x2 + 72x + 20 x -2 - 1 0 2 4 42. f(x ) = 3x3 + 9x2 - 720x- 15 f(x) 2 1 2