Given facts about f (x) and number lines for f'(x) and f" (x) , analyze the function f (x) and sketch a possible graph of f (x). Identify all maximums, minimums, and points of inflection. 1. f (x) is continuous everywhere and 2 . f (x) is continuous everywhere, but differentiable everywhere. not differentiable x =3 and x =1. lim = -3 and lim =3 BI x -7 00 -2- 3. * -+ 3 " x-+1 lim f (x)=co, lim f (x) = DNE, and lim f (x) =co. f (x) is continuous and differentiable elsewhere. lim f (x) =0 f(0) =2 x ->1 00 3 - s' ( x ) + UX 2= - 2 -17 - 2 - -3- 5-If the given graph of f'(x) , sketch a possible graph of f (x). (Analyze f' and f" number lines to do this.) 1. AY f' (x) 2 . f' (x) -54 3 -2 0 1 2 345 -4 -3-2 -1 0 2 3 D + D D -5 4-3 -2 -1 01 2 3 -54-3 -2 -1 012 0 - D + -5 -4 -3 -2 -1 0 1 2 3 45 -5 -4 -3 -2 -1 01 2 7X X -5 4-3 -2 -10 1 2 4 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 AY 3. lim f (x) = 2 x -+too AY f' (x ) - - - - -5 4-3 -2 -1 0 1 2 3 4 -5 4 1 2 3 5 X 5 -4 -3 -2 -1 0 1 2 3 4 5 5 -4 -3 -2 -1 0 1 2 3 5