2x = See CalcChat.com for tutorial help and worked-out solutions to odd-numbered exercises. 47. fx) 48.Hx) = x Think Abou function f Intervals on Which a Function Is Increasing or In Exercises 1-8, n the closed interval. Decreasing In Exercises 21-26, find the open which the function is increasing or decreasing intervals 49. f(0) =f( f(3) = f' f (x) > Of f (x) >0f f (x) < Of f"(x) < 0 on =+6x, [-6, 1] -3 [0,9] 22. h(x) = (x + 2)1/3 +8 21. f(x) = x2 +3x- 12 23. f(x) = (x -1)2(2x 5) 24. g(x) = (x + 1)3 25. h(x) = Vx(x - 3), x > 0 x [0, 2] 0 x< 2T 26. f(x) = sinx + cos x, 1 Applying the First Derivative Test In Exercises 27-34, (a) find the critical numbers of f, if any, (b) find the open intervals on which the function is increasing or (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results f"(x)> Of s9-12, determine to f on the closed decreasing, 51. Writin grow e applied, find all h that f'(c) = 0. If why not. 28. f(x) 4x3- 5x me 27. f(x) = x2- 6x+ 5 3-8x 30. f(x) 29. f(t) = 4 8t 4 x2 - 3x-4 32. f(x) = 31. f(x) = x-2 33. f(x) = , ) cos x-sin x, 3 TX sin 2 , 4) 34. f(x) Exercises 13-18, can be applied to alue Theorem can 2 Motion Along a Line In Exercises 35 and 36, the f s(t) describes the motion of a particle along a line. (a) Fin velocity function of the particle at any time t 0. (b) Identh, the time interval (s) on which the particle is moving in a direction. (c) Identify the time interval(s) on which the par Is moving in a negative direction. (d) Identify the times) a which the particle changes direction. val (a, b) such that 5C positive , explain why not. 35. s(t) 3t - 212 36. S(t) = 613 -8t+ 3 Finding Points of Inflection In Exercises 37-42, find the points of inflection and discuss the concavity of the graph of the function. 37. f(x) = x3 - 9x2 (a) Use the re 38. f(x) = 6x4 -x 39. g(x) = x /x +5 a model of D = at Value Theorem be 40. f(x) = 3x - 5x ar4 41. f(x) = x + cos x, 0, 2T for the S