Consider the function below. f(x) = e^arctan 6x (a) Find the vertical asymptote(

Question

Consider the function below. f(x) = e^arctan 6x (a) Find the vertical asymptote(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) x = _________ Find the horizontal asymptote(s). (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) y = _____ (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) (c) Find the local maximum and minimum values. (If an answer does not exist, enter DNE.) local maximum value ________ local minimum value _______ (d) Find the interval where the function is concave up. (Enter your answer using interval notation.) Find the interval where the function is concave down. (Enter your answer using interval notation.) Find the inflection point. (x, y) = (___________)

Explanation / Answer

Horizontal Asymptodes =DNE

Vertical Asymptodes y=epi/2 and y=e-pi/2

increasing on x>0

Min=e^-pi/2

MAX=e^pi/2

Point of inflection = 0,1

Concave up = (-inf, 0)

Concave down= (0,inf)

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