Determine Where the Graph Of $f(x)=\ln |x-4|$ Is Concave Upward and Where It Is Concave Downward

Multiple Choice

Determine where the graph of $f(x) =\ln |x-4|$ is concave upward and where it is concave downward. Also, find all inflection points of the function.

A) concave downward: $(-\infty,-4)$ and $(4, \infty)$ , concave upward: $(-4,0)$ and $(0,9)$ ; inflection points: $(-4,0)$ and $(4,0)$
B) concave downward: $(-4,0)$ and $(0,9)$ , concave upward: $(-\infty,-4)$ and $(4, \infty)$ ; inflection points: $(-4,0)$ and $(4,0)$
C) concave downward: $(-\infty, 4)$ and $(4, \infty)$ , concave upward: nowhere; inflection points: none
D) concave downward: nowhere, concave upward: $(-\infty, 4)$ and $(4, \infty)$ ; inflection points: none