Consider the function below. f(x) = ln(8 - ln x) (a) Find the vertical asymptote

Question

Consider the function below. f(x) = ln(8 - ln x) (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 decreasing. (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

(a)

x = 0, exp(8)

y = dne

(b)

( 0, exp(8) )

(c)

dne

dne

(d)

( 0 , exp(7) )

( exp(7) , exp(8) )

(x,y) = ( exp(7) , 0 )

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