3x + 5' 180x (x² + 1)(x + 1)(x – 1) (3x* + 5)² .4 and f"(x) = Use these functions 13 (3x +5)* to complete the following steps. a. Find the critical points and possible inflection points of f. b. Find the intervals on which f is increasing or decreasing. c. Determine the intervals on whichf is concave up or concave down. 48. y A d. Identify the local extreme values and inflection points of f. e. State the x- and y-intercepts of the graph of f. f. Find the asymptotes of f. g. Use your work in parts (a) through (f) to sketch a graph of f. y=f'E 15-46. Graphing functions Use the guidelines of this section to make a complete graph of f 15. f(x) = x2 – 6x 16. f(x) = x – x? 17. f(x) = x' – 6x + 9x 18. f(x) = 3x - x' 0. 19. f(x) = x - 6x? 20. f(x) = x + 4x3 21. f(x) = (x – 6)(x + 6)² 22. f(x) = 27(x – 2)²(x + 2) T 49-54. Graphing wit! following functions. A local extreme values, c 23. f(x) = x - 6x² – 135x 24. f(x) = x* + 8x - 270x² + 1 49. f(x) = ' - 2 1 25. f(x) = x' - 3x2 144x- 140 %3D -x3 147x + 286 27. f(x) = x - – 2Vx 50. f(x) = 5 Зх 28. f(x) = 3Vx - x/2 29. f(x) = x² – 1 51. f(x) = 3x + 4x 52. f(x) = x – 33x 2x 3 2x 8 30. f(x) = 31. f(x) = 12 3x 5 x² 1 53. f(x): .2 32. f(x) = 33. f(x) + 12 x²- 4 2x + 1 55. Explain why or w statements are true 4x 34. f(x) = x + 3 35. f(x) = tan a. If the zeros of 36. f(x) = In (x² + 1) are located at th b. If the zeros of f 37. f(x) = x + 2 cos x on [-2T, 27] are also located c. If the zeros of th 38. f(x) = x- 3x²/3 39. f(x) = x – 3x/3 vertical asympto 40. f(x) = 2 - 2x²/3 + x+/3 41. f(x) = sin x – x on [0, 27] d. If a rational fund have a finite lim