Question

f(x)=e^arctanx
a.)find the vertical and horizontal asymptotes
b.) find the intervals of increase and decrease
c. find the local maximum and minimum vaules
d.) find the intervals of concavity and the inflection points

Answer 1

Vertical asymptotes: What values of \(x\) (if any) make the function undefined?

Horizontal asymptotes: What's the end behavior of the function? i.e. what can you say about the function given the values of the limits (if they exist)
\[\large\lim_{x\to-\infty}e^{\arctan x}\quad\text{and}\quad\lim_{x\to\infty}e^{\arctan x}\]
What's the first derivative? Second derivative?