Posted by Anonymous on Monday, April 5, 2010 at 5:01pm.
to have a vertical asymptote, 1 + e^x has to be zero, or
e^x = -1
No value of x makes that statement true, so there is no vertical asymptote.
for x --->∞ , f(x) approaches 1
for x ---> -∞, f(x) approaches 0
so for large +x's, the horizontal asymptote is y = 1
for large -x's the horizontal asymptote is y = 0
f'(x) = [(1+e^x)(e^x) - e^x(e^x)]/(1+e^x)^2
= e^x(1 + 2e^x)/(1+e^x)^2
This will always be positive for any value of x, so the function is increasing for all values of x
so would the inflection points be (0,1)?
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