# Suppose we know the following information about the function f. •the domain of f is (−∞,−1)∪(−1,∞) •f(0) = 0, f(1) =1/2 •f′(−1) is undefined, f′(0) = 0 •f′(x)>0 on (−∞,−1) and (0,∞). ,

Suppose we know the following information about the function f.

•the domain of f is (−∞,−1)∪(−1,∞)

•f(0) = 0,     f(1) =1/2

•f′(−1) is undefined,       f′(0) = 0

•f′(x)>0 on (−∞,−1) and (0,∞).    ,f′(x)<0 on (−1,0)

•f′′(−1) is undefined,   f′′(1) = 0.

•f′′(x)>0 on (−∞,−1) and (−1,1),       f′′(x)<0 on (1,∞)

•limx→−1f(x) =∞,        limx→±∞f(x) = 1

(1) Find the equation of any vertical asymptotes of f.

(2) On what intervals is f increasing or decreasing?

(3) Find the local maximum and minimum function values of f, and indicate where they occur.

(4) On what intervals isfconcave up or down?

(5) Find all inflection points of f.

(6) Find the equation of the horizontal asymptote of f, or indicate that there is no horizontal asymptote.

(7) Sketch a graph of y=f(x). Label all local max and mins, points of inflection, and asymptotes.

(550 words)

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