1. Sketch the graph of a function f based on the following information. Show intervals of increase and decrease, and concavity. Label all local maxima and minima and points of inflection, and any asymptotes. f' (x) = (x+1)ex lim f(x) = 0 f"(x) = (x+2)ex x - -00 f (0) = 0 lim f (x) = co x -+ 00 2. Sketch the graph of a function f based on the following information. Show intervals of increase and decrease, and concavity. Label all local maxima and minima and points of inflection, and any asymptotes. Your sketch should also include the tangent line to f at the point (0,1) f(0) = 1 lim f(x) = 1 x + 00 4 f' (xx) = lim f(x) = 1 x2 - 4 x - -00 -8x lim f(x) = 00 f" (x) = x - -2 (x2 - 4) 2 lim f (x) = - 00 r - 2 3. Sketch the graph of a function f on the interval [0,2x], using the following information. Show intervals of increase and decrease, and concavity. Label all local maxima and minima and points of inflection, and any asymptotes. f'(x) = cos(x)+5 f(0) = 2 f (IT) = 3.57 f"(x) = -sin (x) f (2n) = 5.14