y = 8"(x) maximum wo roots. reasing? maximum? 15. Is it possible for a function to satisfy f(x) > 0, f'(x) > 0, and f"(x) 0 and f"(x) 0 and f"(c) = 0, then f has a local maximum at c. 57. A(r) = 24/r + 2Tr2, r > 0 c. Two functions that differ by an additive constant both increase and decrease on the same intervals. 58. f(x) = xV3 - x d. If f and g increase on an interval, then the product fg also in- 59-62. Sketching curves Sketch a graph of a function f that is con- creases on that interval. tinuous on (-oo, co ) and has the following properties. e. There exists a function f that is continuous on ( - oo, x ) with exactly three critical points, all of which correspond to local 59. f' (x) > 0, f"(x) > 0 maxima. 60. f'(x) 0on (-0, 0); f'(x) > 0 and f"(x) > 0 on (0, 0o ) 96-97. Functions from derivatives Consider the following graphs of f' and f". On the same set of axes, sketch the graph of a possible fune 61. f'(x) 0 tion f. The graphs of f are not unique. on (0, 00 ) 96. 97. 62. f'(x) 0 on (-co, 0); f'(x)