Consider the function below. (Round the answers to two decimal places. If you need to use - or , enter -INFINITY or INFINITY.)

Question

f(x) = e^x/1+e^x
find the horizontal and vertical assymptotes?
find the interval whr f is increasing?


Find the inflection point.

Find the interval where the function is concave up.

Find the interval where the function is concave down.

Answer 1

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

Answer 2

so would the inflection points be (0,1)?