1. Let f be a function satisfying the following properties: • continuous on R\{1} • f(0) = 0 and f(3) = 7 • lim f(x) = +o lim [f(x) – (x + 2)] = 0 lim [f(x) – (x + 2)] = 0 Moreover, the table of signs for f' and f" is given below. (-∞0, 0) | 0 | (0, 1) 1 (1,3) | 3 | (3,+∞ f'(r) f"(x) + + und. + + und. + + 1. Give equations of the two linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up or concave down. Determine the relative maximum, relative minimum and inflection points of the graph of f (if any). 3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.

1. Let f be a function satisfying the following properties: • continuous on R\{1} • f(0) = 0 and f(3) = 7 • lim f(x) = +o lim [f(x) – (x + 2)] = 0 lim [f(x) – (x + 2)] = 0 Moreover, the table of signs for f' and f" is given below. (-∞0, 0) | 0 | (0, 1) 1 (1,3) | 3 | (3,+∞ f'(r) f"(x) + + und. + + und. + + 1. Give equations of the two linear asymptotes of the graph of f. 2. Determine where is f increasing or decreasing and concave up or concave down. Determine the relative maximum, relative minimum and inflection points of the graph of f (if any). 3. Sketch the graph of f with emphasis on concavity. Label all the relative extremum points, and inflection points with their respective coordinates, and the asymptotes with their respective equations.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 35E

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